HARTZ, Circuit Judge.

Defendant Fabian Dunbar pleaded guilty in the United States District Court for the District of Kansas to distributing cocaine. The plea was conditioned on the district court's imposing a sentence of 48 months' imprisonment, as set forth in a plea agreement between Defendant and the government under Fed.R.Crim.P. 11(c)(1)(C). The agreement also stated that the parties would recommend a consecutive sentence of 12 months' imprisonment for Defendant's violating his supervised release from a 2006 sentence. The agreement did not include a waiver of Defendant's right to appeal.

The district court set the same time for hearings to sentence Defendant on the drug-distribution charge and to consider the petition charging him with violations of his supervised release. The court announced that it would begin with sentencing on the drug charge. But when it asked whether defense counsel had any objections to the presentence report (PSR), defense counsel responded that Defendant was dissatisfied with his performance and wanted new counsel. During the ensuing discussion of whether to replace defense counsel, Defendant submitted a pro se pleading that complained of counsel's performance in connection with his guilty plea and asserted that Defendant had "mental disabilities." R., Vol. 1 at 75. After further discussion the court ruled that counsel should continue representing Defendant and sentenced Defendant to 48 months' imprisonment on the drug charge.

Next the court turned to the charges that Defendant had violated the terms of supervised release. It found that Defendant had committed the violations, but it declined to accept the parties' recommendation of a 12-month sentence and proposed three years. Defendant protested that his counsel had assured him that the recommended 12-month sentence was binding on the court, and asserted that he would have gone to trial on the drug-distribution charge if he had known that he could receive a sentence of more than 12 months' imprisonment for violating his supervised release. Defense counsel denied telling Defendant that the recommendation was binding, and the court sentenced Defendant to 36 months' imprisonment, to run consecutively to his 48-month sentence.

Defendant appeals both his distribution conviction and the revocation of supervised release. He raises four challenges: (1) that the district court conducted an inadequate inquiry into his request for new counsel and abused its discretion in denying his request; (2) that the district court abused its discretion in failing to construe his pro se pleading and various oral protests as motions to withdraw his plea; (3) that his plea was not knowing and voluntary because his counsel had given him inaccurate information; and (4) that his sentence on revocation of supervised release was procedurally and substantively unreasonable.

Exercising jurisdiction under 28 U.S.C. § 1291, we affirm. First, the district court conducted an adequate inquiry into Defendant's request for new counsel, and did not abuse its discretion in denying the request because defense counsel's explanation could persuade a reasonable jurist that counsel's performance had been satisfactory and that any failures of communication had been Defendant's fault. Second, the court did not err in declining to treat Defendant's pro se pleading and oral statements as motions to withdraw his plea because Defendant was represented by counsel who did not make a timely motion to permit withdrawal of the plea and Defendant's statements in any event were unclear or untimely. Third, Defendant did not raise in district court a challenge to the validity of his plea, and there is no plain error because the pertinent facts are not established in the record. And fourth, as to Defendant's sentence on violation of the terms of supervised release, he has failed to show plain error with respect to the procedural reasonableness of his sentence and his sentence was not substantively unreasonable.

I. BACKGROUND

A. Proceedings Before Plea to 2011 Drug Charge

In August 2006 Defendant pleaded guilty to the offense of possession of five grams or more of cocaine base with intent to distribute (the 2006 Conviction). See 21 U.S.C. § 841(a)(1). He was eventually sentenced to 60 months' imprisonment, to be followed by a term of four years' supervised release. In November 2009 Defendant was transferred from a prison to a halfway house to complete his sentence. He was released from the halfway house and placed on supervised release in May 2010.

That December Defendant was indicted for being a felon in possession of a firearm. The government also filed a petition to revoke his supervised release, alleging his firearm offense, failure to report in person to the probation office, and failure to inform the probation office that he had left his job.

In a separate indictment filed the next month, Defendant was charged with conspiring between January 2009 and May 2010 to manufacture and distribute 50 grams or more of cocaine base. See id. § 841(a)(1), (b)(1)(A)(iii); id. § 846. Because Defendant had a prior felony drug conviction, he faced a statutory mandatory-minimum sentence of 10 years' imprisonment and a maximum sentence of life imprisonment. See id. § 841(b)(1)(B)(iii).

The district court held separate trials on the gun-possession and drug-conspiracy charges. A jury acquitted Defendant of the gun-possession charge. At the conspiracy trial the jury deadlocked, and the judge declared a mistrial.

B. Plea Agreement

Defendant then engaged in plea negotiations with the government. To encourage a guilty plea, the government stated that before any retrial it would file a superseding indictment charging Defendant with a drug offense that would carry a mandatory minimum sentence of 20 years' imprisonment. The parties reached an agreement, and on September 19, 2011, the government filed a superseding information accusing Defendant of distributing and possessing with intent to distribute an unspecified amount of cocaine base (carrying no mandatory minimum sentence, see id. § 841(b)(1)(C)), and Defendant filed a petition to enter a guilty plea to the information. Under the agreement the government would dismiss the conspiracy count in the indictment. Further, the parties agreed to a 48-month sentence under Fed.R.Crim.P. 11(c)(1)(C), recognizing that Defendant could withdraw his guilty plea if the district court did not agree to the stipulated sentence. See Fed. R.Crim.P. 11(c)(5), (d)(2)(A). They also agreed to recommend a sentence of 12 months' imprisonment for Defendant's violation of his supervised release from his 2006 Conviction.1

After conducting a plea colloquy the district court found that Defendant was competent to enter the plea, had entered the plea knowingly and voluntarily, and was guilty of the offense.

C. The Sentencing Hearing

The district court (although not the judge who had accepted the plea) set the same time for sentencing on the 2011 drug charge and the hearing on the petition to revoke Defendant's supervised release. Soon after the court announced that it would start with the sentencing, defense counsel stated that Defendant was dissatisfied with his representation and wanted new counsel appointed for him. He said that Defendant was "not listening at all," R., Vol. 2, pt. 5 at 808, and explained:

Id. at 809-10. The court asked Defendant why he was worried about the drug amounts in the PSR when they would make no difference to his sentence if it accepted the plea agreement. But Defendant was not responsive. He said:

Id. at 810-11. Defendant also argued that his counsel should have objected to other matters in the PSR. After his counsel said that Defendant was referring to paragraphs 52 and 53 of the PSR, the court questioned Defendant about what was erroneous in those paragraphs. Although Defendant raised one complaint, the PSR conformed to what he asserted and ultimately he responded only, "I don't know." Id. at 814.

Defendant also expressed confusion about the guidelines recommended sentence for violating his supervised release:

Id. at 815. Defense counsel explained that earlier that day he had told Defendant that although the parties would recommend a 12-month sentence on revocation, the guidelines range was actually 15 to 21 months. But the prosecutor corrected him, stating that the true range was 8 to 14 months. The court confirmed that the recommended sentence fell within the guidelines range, and asked defense counsel and the prosecutor whether the recommended sentence was binding. Both said it was not, and defense counsel added, "And that's what I explained to Mr. Dunbar as well." Id. at 818. The court then asked Defendant, "So what's the problem?" Id. He responded: "I ain't got nothing to say." Id.

At that point Defendant handed the court a hand-written pro se pleading titled, "Judicial Notice of Adjudicative Facts and Preserving of All Appealable Issues" (the Pro Se Pleading), which listed grievances with his counsel, id., Vol. 1 at 75; it said:

Id. After the court summarized the pleading, Defendant explained: "I just said I'm talking about my appeal rights.... He told me I have my appeal rights even though I took a plea in this case." Id., Vol. 2, pt. 5 at 820. The court responded, "I'm sorry, did you say appeal rights?" Id. And when Defendant answered yes, the court said, "Okay. So we will docket this as a Notice of Appeal." Id.

After this exchange the court asked Defendant whether he suffered from mental disabilities, as he had stated in his Pro Se Pleading, and whether he was "competent to go forward with sentencing." Id. Defendant said that he suffered from mental disabilities and could not "really read," id., but he did not know if he was competent to proceed. The court then turned to defense counsel, who described Defendant as mentally competent:

Id. at 821-22 (emphasis added).

The court asked Defendant whether he agreed with his counsel's assessment. In the exchange that followed, Defendant said: "I only got a learning disability.... Reading and paying attention — like — it's like reading and it's like learn or not. I can't really focus that much, you know, I had a hard time." Id. at 823. Defendant's mother, who was in the courtroom, added that Defendant had suffered from mental disabilities as a child:

Id. at 824. The court concluded that it would not replace defense counsel because Defendant had not "shown good reason to substitute" his attorney so late in the proceedings. Id. at 827.

The court turned to the merits of the plea agreement, hearing from counsel and offering Defendant an opportunity to speak. It accepted the plea agreement and sentenced Defendant to 48 months' imprisonment and six years' supervised release on the 2011 charge.

Next the court considered the charge that Defendant had violated the terms of his supervised release from his 2006 Conviction. Defense counsel stipulated that Defendant had violated his supervised release by committing the crime charged in the 2011 information (which actually occurred before the commencement of his supervised release) and by failing to report to probation officers. And the court found that he had committed the firearm offense of which he had been acquitted.

The court informed the parties that it intended to reject the parties' recommended sentence of 12 months' imprisonment and instead impose a sentence of 36 months, which was the statutory maximum because his conviction had been for a Class B felony. See 18 U.S.C. § 3583(e)(3). When the district court asked Defendant if he wanted to say anything, he claimed that he had agreed to at most a one-year sentence for violating his supervised release:

R., Vol. 2, pt. 5 at 850.

The court questioned Defendant further, but he continued to insist that he "would have just went to trial" if he had known that the 12-month sentence was not binding. Id. at 851. It then asked defense counsel again whether he had explained to Defendant that the 12-month sentence for violating his supervised release, although recommended by the parties, was not binding on the court. Defense counsel asserted that he had properly informed Defendant:

Id. at 856.

Defendant, however, continued to assert that he had been misled and would not have pleaded guilty if he had understood the plea agreement. The court told him that "[i]f your guilty plea was not a knowing plea and a voluntarily [sic] plea, then you should file a motion to vacate it and then the Court will decide whether to vacate it or not," id. at 859, but it advised him that "you need to talk with your attorney about this," id., and noted that "[i]t's not necessarily in your best interests to get the plea vacated because you got a very favorable agreement here with the government," id.

Defendant then protested that he was innocent, claiming, "I never messed up on supervised release — I reported, monthly report, I did all of that with no problem and no dirties or nothing.... I wasn't selling no drugs. I just plead to it." Id. at 861. The district court told Defendant that he should talk to his lawyer before "continu[ing] along these lines" because he was likely violating the plea agreement, id. at 862, and sentenced him to three years' imprisonment. After sentence was pronounced, Defendant said: "I can't understand. I might as well just take my plea back." Id. at 865. The court responded: "You don't have the right to take your plea back." Id.

Defendant raises four grounds for reversal: (1) that the district court conducted an inadequate inquiry into his request for new counsel and abused its discretion in denying his request; (2) that the district court abused its discretion in failing to construe the Pro Se Pleading and various oral statements as motions to withdraw his plea; (3) that his plea was not knowing and voluntary because he thought that the 12-month recommendation was binding on the court, and his counsel misinformed him of his sentencing exposure if the government filed a superseding indictment; and (4) his sentence on revocation of supervised release was procedurally and substantively unreasonable. We address each argument in turn.

II. DISCUSSION

A. Denial of Motion to Substitute Counsel

"To warrant a substitution of counsel, the defendant must show good cause, such as a conflict of interest, a complete breakdown of communication or an irreconcilable conflict which leads to an apparently unjust verdict." United States v. Lott, 310 F.3d 1231, 1249 (10th Cir.2002) (internal quotation marks omitted). "[M]ere strategic disagreement between a defendant and his attorney" is not enough to show good cause; "rather, there must be a total breakdown in communications." Id. When presented with a motion to substitute counsel, "[t]he district court is under a duty to make formal inquiry into the defendant's reasons for dissatisfaction with present counsel." United States v. Anderson, 189 F.3d 1201, 1210 (10th Cir. 1999) (internal quotation marks omitted). We review for abuse of discretion. See United States v. Hutchinson, 573 F.3d 1011, 1024 (10th Cir.2009). "It is only when the district court's decision is legally erroneous, or when the facts are so lopsided against the option the district court has chosen (even when abiding the rule a district court's factual findings may be reversed only when clearly erroneous), that we reverse." Id. We examine (1) the timing of the motion, (2) the adequacy of the trial court's inquiry into the reasons for the motion, (3) "whether the defendant-attorney conflict was so great that it led to a total lack of communication precluding an adequate defense," and (4) "whether the defendant substantially and unreasonably contributed to the communication breakdown." Lott, 310 F.3d at 1250. In the absence of specific findings by the court, we construe the evidence in the light most favorable to the court's ruling. See United States v. Jenkins, 175 F.3d 1208, 1212 (10th Cir.1999).

Defendant argues that he demonstrated good cause for substitution of counsel because: (1) he lost faith in his counsel; (2) there was no meaningful communication between Defendant and his counsel; and (3) Defendant had legitimate reasons for losing faith in his counsel because counsel (a) had failed to object to the drug amounts and criminal-history score in the PSR, (b) did not meet with Defendant about the PSR until after the objections were due, (c) did not inform Defendant of the possible length of his sentence on revocation, (d) described Defendant as "extremely bright," R., Vol. 2, pt. 5 at 822, even though he was "functionally illiterate and mentally disabled," Aplt. Br. at 54, and (e) stipulated to Defendant's violation of his supervised release even though Defendant claimed he was innocent. And he contends that the district court conducted an inadequate inquiry into his request for substitution of counsel because it (1) denied the motion without fully understanding the basis of Defendant's complaints, (2) focused on Defendant's objections to the PSR rather than his problems with counsel, and (3) put the burden entirely on Defendant to explain why substitution was appropriate even though his ability to express himself was hampered by his mental retardation.

We are not persuaded. We begin with the claims of deficient representation. The district court could properly find that defense counsel's performance had been satisfactory. Defendant has not explained what purpose would have been served by his counsel's challenging anything in the PSR; his stipulated sentence was not based on the PSR, and, as the court noted, had it rejected the plea agreement, Defendant would have gone back to square one and have had the opportunity to challenge the PSR if later found guilty. Likewise, there was no reason for counsel to meet with Defendant about the PSR before the sentencing hearing. Also, if the court believed the representations of counsel, as it could reasonably do, then Defendant had been told that he was not guaranteed a one-year sentence on revocation, and was competent to understand the plea agreement. As to the assertion that counsel had improperly stipulated to violations of his supervised release, the stipulation occurred after the court had denied the motion to replace counsel, so it is irrelevant to our review of the denial. But in any event, Defendant voiced no objection at the time of the stipulation, he had already admitted to his drug-distribution offense, and he did not assert his innocence until he was informed of his sentence on revocation. The court consequently had no reason to believe that counsel's stipulation had been contrary to Defendant's wishes. Thus, the record supports a determination that Defendant had no justification for losing faith in his attorney. And the court could reasonably credit counsel's comments to the effect that Defendant was the one solely responsible for any failure of communication. See Lott, 310 F.3d at 1250 (court must examine "whether the defendant substantially and unreasonably contributed to the communication breakdown").

We likewise see no merit to Defendant's argument that the district court's inquiry was inadequate. The court afforded defense counsel and Defendant ample opportunity to explain Defendant's grievances. That Defendant was unpersuasive was not because he was denied the chance to express himself. There is no reason to believe that the court did not understand Defendant's complaints or ignored any of them. As to Defendant's contention that because of his alleged mental retardation the court should not have imposed on him the burden of showing the need for new counsel, his briefs on appeal do not point to any concerns with counsel that Defendant failed to articulate during the hearings. We conclude that the court's inquiry was "sufficient to explore and understand the defendant's concerns about the inadequacy of counsel." United States v. Vargas, 316 F.3d 1163, 1166 (10th Cir.2003); see Lott, 310 F.3d at 1249 n. 15 (when a defendant's reasons for withdrawal are "insubstantial" and he received "competent representation," no further inquiry is required (internal quotation marks omitted)); United States v. Beers, 189 F.3d 1297, 1302 (10th Cir.1999) (district-court inquiry into defendant's eve-of-trial motion to substitute counsel was adequate even though it did not afford defendant himself an opportunity to speak; defense counsel informed the district court of defendant's reasons, and those reasons were not substantial); United States v. Johnson, 961 F.2d 1488, 1491 (10th Cir.1992) (district-court inquiry into defendant's motion to substitute counsel was sufficient when the court afforded defendant the opportunity to explain his grievances with counsel and those grievances did not show good cause).

In short, the district court did not abuse its discretion in refusing to provide new counsel to Defendant at such a late stage of the prosecution.

B. Motion to Withdraw Guilty Plea

Defendant argues that his Pro Se Pleading and oral statements should have been interpreted as motions to withdraw his guilty plea and that the district court abused its discretion in failing to consider them and grant withdrawal. He admits that the Pro Se Pleading did not "expressly request" withdrawal of his plea, but contends that his allegations that defense counsel had induced him to plead guilty "could mean nothing else." Aplt. Br. at 50. And he contends that "he repeated [his request to withdraw his plea] over and over through the course of the hearing." Id.

We disagree. To begin with, when Defendant submitted his Pro Se Pleading the matter before the district court was whether his counsel should be replaced. Unless that issue was resolved by permitting him to proceed pro se, Defendant had no right to submit motions other than through his attorney. See United States v. Jarvi, 537 F.3d 1256, 1262 (10th Cir.2008) (court has discretion to refuse to consider pro se motion submitted by defendant with counsel); United States v. Bennett, 539 F.2d 45, 49 (10th Cir.1976) (same). And if the trial judge has no duty to consider pro se motions by a represented defendant, she likewise has no duty to investigate whether the defendant is trying to make a pro se motion.

Moreover, the pleading spoke in terms of Defendant's complaints about counsel, not withdrawal of the plea; and when asked about the pleading by the district court, Defendant responded, "I just said I'm talking about my appeal rights.... He told me I have my appeal rights even though I took a plea in this case." R., Vol. 2, pt. 5 at 820. The court accepted the pleading as a notice of appeal. (Filing a notice of appeal could not prejudice Defendant.) The court acted reasonably in not construing Defendant's pleading as a pro se motion to withdraw his plea. And if it had viewed it as such a motion, we can be confident that it would have exercised its discretion by refusing to consider it: when Defendant was later explicit in expressing regret about his plea, the court, after pointing out that withdrawal of the plea would void a very favorable plea bargain, suggested to Defendant that he consult with his attorney.

As for the later oral statements by Defendant that he asserts should have been treated as motions to withdraw his plea, not only were they not framed as motions (they expressed discontent but did not request relief), but even if considered to be motions, they were pro se motions by a defendant represented by counsel. And they were untimely; all were made in response to the district court's declaration that it intended to impose a 36-month sentence for violating the terms of supervised release, after Defendant had already been sentenced on the drug-distribution charge. See Fed.R.Crim.P. 11(e) ("After the court imposes sentence, the defendant may not withdraw a plea of guilty or nolo contendere, and the plea may be set aside only on direct appeal or collateral attack."). In sum, we see no error in the district court's not treating Defendant's written and oral communications as motions to withdraw his plea.

C. Voluntariness of Plea to 2011 Charge

To be valid, a guilty plea must "represent[ ] a voluntary and intelligent choice among the alternative courses of action open to the defendant." Hill v. Lockhart, 474 U.S. 52, 56, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985) (internal quotation marks omitted). Defendant argues that his plea to the 2011 offense was involuntary because (1) he did not understand that the trial court could sentence him to more than 12 months on the supervised-release violation, and (2) defense counsel misinformed him of the mandatory-minimum sentence that the government could impose if it filed a superseding indictment.

These arguments were not properly presented in the district court. The court did not err in failing to treat Defendant's Pro Se Pleading or any of his later oral complaints as a motion to withdraw his plea because, as explained above, the court need not consider pro se motions by represented defendants, the purported motions were not clearly motions, and most of the purported motions were untimely. Nor has Defendant pointed to a proper motion in district court challenging his plea. Accordingly, our review is only for plain error. See United States v. Weeks, 653 F.3d 1188, 1198 (10th Cir.2011). We are particularly reluctant to hold that a pro se motion by a represented defendant preserves an issue for appeal because to do so is to instruct district courts that they must consider and resolve such pro se motions. If such a motion preserved an issue even if the trial court exercised its discretion not to address the motion, we could not impose the restrictions attendant to plain-error review and would ordinarily (unless the motion was patently meritless) have to remand for a hearing on the motion if the issue was pursued on appeal. District courts would soon learn that the more efficient approach would be to rule on all pro se motions.

"Plain error occurs when there is (1) error, (2) that is plain, which (3) affects the defendant's substantial rights, and which (4) seriously affects the fairness, integrity, or public reputation of judicial proceedings." Id. (internal quotation marks omitted). The obstacle that Defendant cannot surmount is the second requirement of plain-error review — namely, that the alleged error is plain. When the existence of an error depends on what the facts are — such as whether defense counsel informed the defendant of the maximum possible sentence — the error cannot be said to be "plain" unless the facts are uncontestably established, either because they are undisputed or undisputable or because the factfinder made a proper finding of fact. The error is not "plain" if the "fact" establishing the error may be false. As we have stated:

United States v. Lewis, 594 F.3d 1270, 1288 (10th Cir.2010); see United States v. Frost, 684 F.3d 963, 977 (10th Cir.2012) ("Where the determinative facts are missing from the record due to the defendant's failure to make a timely objection, we will not find plain error based on the possibility that better factual development would have made the error clear."). A disputed assertion of fact cannot support a claim of plain error except in the rare case — not present here — where "the appellant can establish the certainty of a favorable finding on remand." Lewis, 594 F.3d at 1288.

Here, there is no such certainty that there would be a finding favorable to Defendant on remand. To be sure, some of Defendant's own statements support his contentions. But they are not unchallenged. Defendant's attorney twice told the district court that he had properly informed Defendant that the 12-month sentence was not guaranteed. Most relevant, on the first occasion, before Defendant was sentenced on the drug charge, Defendant voiced no objection to his attorney's statement, responding only "I ain't got nothing to say" when the court asked "So what's the problem?" R., Vol. 2 pt. 5 at 818. Nor is the record clear that defense counsel misinformed Defendant about the potential mandatory minimum sentence; counsel told the court only that he had "talked to [Defendant] specifically about the 20 years mandatory minimum if he was found guilty" under the superseding indictment. Id. at 855.

D. Sentence on Revocation of Supervised Release

Defendant challenges his three-year sentence for violating the terms of his supervised release as both procedurally and substantively unreasonable. We are not persuaded.

Defendant argues that his sentence is procedurally unreasonable because (1) the district court failed to take into account his mental retardation in sentencing him and did not read the PSR; (2) the court failed to consider the guidelines policy statements for supervised-release violations; and (3) the court premised its sentencing decision on the mistaken belief that Defendant had committed his new drug offense while on supervised release. These arguments, however, were not presented to the district court. Therefore our review is for plain error. See United States v. Ruby, 706 F.3d 1221, 1225-26 (10th Cir.2013).

We easily dispose of Defendant's first two arguments because they lack a proper factual basis. Absent argument on these matters at sentencing, the district court had no obligation to say that it was taking Defendant's mental deficiencies into account, that it had read the PSR, and that it had considered the guidelines policy statements. See United States v. Pinson, 542 F.3d 822, 833-36 (10th Cir.2008) (Sentencing court that varies from the guidelines need not discuss every § 3553(a) factor but need only state its reasons for varying and address defendant's material, nonfrivolous arguments.); United States v. Zuniga-Chavez, 464 F.3d 1199, 1202 (10th Cir.2006) ("The sentencing court is not required to consider individually each factor listed in § 3553(a) before issuing a sentence. Moreover, we do not demand that the district court recite any magic words to show that it fulfilled its responsibility to be mindful of the factors that Congress has instructed it to consider." (brackets and internal quotation marks omitted)). Therefore, we cannot presume from the court's silence that Defendant's allegations are true. Indeed, the evidence in the record suggests otherwise; for example, the court apparently had read the PSR because it referenced specific facts from the PSR during its comments. We will not remand for an evidentiary hearing on whether the district court considered Defendant's mental condition or the guidelines policy statement, because the very fact that the court could well state on remand that it did consider them is enough to establish that the alleged errors could not be "plain." See Frost, 684 F.3d at 977; Lewis, 594 F.3d at 1288.

Defendant's third argument requires further discussion. He argues that the district court's "sentencing decision... rested on a significant factual error, namely, [its] belief that [Defendant] committed the new drug offense while on supervised release, when in fact his alleged drug activities had ended before his supervised release began." Aplt. Br. at 58. Defendant is correct (1) that he committed the drug offense while he was still at the halfway house and before his term of supervised release, and (2) that the district court incorrectly assumed that Defendant had committed the offense while on supervised release. The court's error, however, appears to have been an invited one. At the outset of the proceedings on revocation, immediately after Defendant was sentenced on his drug offense, defense counsel stated:

R., Vol. 2, pt. 5 at 843-44. This was error, because the probation-office petition for revocation referenced only the firearms charge and failures to communicate with the probation office, not the drug charge, and the plea agreement did not state the grounds for revocation. Invited errors are waived and not grounds for reversal. See United States v. Lopez-Medina, 596 F.3d 716, 733 n. 10 (10th Cir.2010) ("[T]he invited-error doctrine ... prevents a party from inducing action by a court and later seeking reversal on the ground that the requested action was in error." (internal quotation marks omitted)). Further, Defendant has not satisfied his burden under plain-error review to show that he was prejudiced by the court's error. The district court found that Defendant had committed the violations alleged in the revocation petition. And we have no reason to believe that the court would have imposed a lesser sentence if it had been advised that the drug offense predated Defendant's supervised release. Indeed, defense counsel was probably incautious when he made his error because the accuracy of his statement was inconsequential.

As for Defendant's claim of substantive unreasonableness, he argues that his mental retardation so diminishes his personal culpability that the three-year sentence must be set aside. But we can reverse only if the sentence, in light of the sentencing factors referenced in 18 U.S.C. § 3583(e), was an abuse of discretion because it was "arbitrary, capricious, whimsical, or manifestly unreasonable." United States v. Damato, 672 F.3d 832, 838 (10th Cir.2012) (internal quotation marks omitted). In light of Defendant's criminal history, as well as his denial of responsibility at the sentencing hearing, we cannot say that the sentence was an abuse of discretion. It was eminently reasonable to believe, as the district court did, that Defendant would continue his criminal ways if not incarcerated because he had "already squandered a chance to show that he is capable of leading a law-abiding life and following the terms of supervision and working with the Probation Office." R., Vol. 2, pt. 5 at 849-50. Although retardation may reduce culpability, it need not override all other proper sentencing considerations.

III. CONCLUSION

We AFFIRM the judgment of the district court.