OPINION

By the Court, PICKERING, C.J.:

On this appeal we consider NRS 286.541(2), governing retirement by members of the Public Employees' Retirement System (PERS). PERS interprets NRS 286.541(2) as limiting retirement eligibility. In its view, a member who goes from one PERS-eligible job to another without a break in service and retiring from PERS may not thereafter retire and receive benefits from PERS, until the member effectively retires from his or her new PERS-eligible job. A contrary interpretation, PERS maintains, would allow in-service distributions, violating NRS 286.541 and the Internal Revenue Code plan-qualification provisions on which PERS depends.

The district court disagreed. In its view, NRS 286.541(2) determines retirement benefit dates, not retirement eligibility. Thus, the district court held that PERS should have allowed respondent Douglas Smith to retire and receive benefits from PERS based on his prior public service, even after he was sworn in as a district court judge, another PERS-eligible position. The district court also held that, under NRS 286.190(3)(a), PERS could and should have equitably excused Judge Smith's noncompliance with NRS 286.541, and allowed him to reverse his eventual election to transfer from PERS to the Judicial Retirement System (JRS), despite NRS 1A.280(6), which makes such an election irrevocable.

The district court erred in its interpretation of the controlling statutes and in reviewing the PERS Board's decision de novo, rather than deferentially. We therefore reverse and reinstate the PERS Board's determination that Judge Smith is not eligible to receive retirement benefits at this time.

I.

Public Employees' Retirement System members may not receive PERS retirement benefits until they effectively retire from PERS. NRS 286.541.1 Under NRS 286.520(1)(a)(2), benefit payments ordinarily cease if a retired employee resumes work for a PERS-eligible employer. But NRS 286.520(5) provides an exception for "a retired employee [who] is chosen by election or appointment to fill an elective public office." Such a retired employee may continue receiving PERS benefits, so long as the new office is not the same as the office in which the employee earned the benefits.

In this case, respondent Douglas Smith meant to avail himself of NRS 286.520(5). A sitting justice of the peace with 23 years of creditable PERS service, Judge Smith ran for and was elected to the Eighth Judicial District Court in November of 2008. He planned to retire as a justice of the peace, start receiving benefits (reduced for early retirement) from PERS, take office as a district court judge, and then elect to participate in JRS rather than PERS.2 Judge Smith believed that this would allow him to receive PERS retirement benefits, in addition to his district judge salary, while accruing a second set of retirement benefits under JRS, eventually receiving benefits under both PERS and JRS.3

Judge Smith consulted PERS staff in November and December 2008 about retirement options. He received estimates based on different scenarios, using an expected retirement date of December 31, 2008. PERS staff also provided Judge Smith with materials explaining how PERS determines effective retirement dates and the implications of taking other public employment before and after retiring from PERS. The PERS Preretirement Guide includes a section, "Some Pitfalls and How to Avoid Them," which cautions: "As we have stated before, your effective date of retirement is the day after your last day of employment, the day your application is received [by] PERS ..., or the date requested on the application, whichever is later.... You must take the initiative. No one will automatically do it for you, and no one, including your public employer, can file your retirement paperwork." Public Employees' Retirement System of Nevada, Preretirement Guide 13 (March 2008 revision).

Separately, Judge Smith consulted Clark County about health insurance. Justices of the peace are paid by the County, while district judges are paid by the State, and Judge Smith faced a gap between plans. Judge Smith learned that he could extend his and his family's County-paid health insurance up to February 1 if he continued as a justice of the peace into January. Under the Nevada Constitution, Article 6, Section 5, Judge Smith's term as a district judge began, and he was sworn in, on January 5, 2009, the first Monday in January. To maximize his insurance coverage, Judge Smith provided a resignation letter to Clark County designating Sunday, January 4, 2009, as his last day as justice of the peace. Clark County reported Judge Smith's termination date as January 4, 2009, and afforded him insurance coverage through January 31, 2009. Judge Smith received his last Clark County paycheck on December 19, 2008.

Judge Smith waited until January 8, 2009, to file the papers required to retire from PERS.4 By then, he had been sworn in as a district court judge. In that capacity, he was employed by a PERS-eligible employer and earning creditable service with PERS. After research, PERS staff determined that, consistent with NRS 286.541(2), Judge Smith could not retire from PERS while employed in a PERS-eligible position. PERS therefore denied Judge Smith's application for retirement benefits.

Judge Smith appealed staffs determination to the PERS Board. At the PERS Board hearing, Judge Smith cited NRS 286.190(3)(a) and asked for an equitable exception to NRS 286.541(2). He acknowledged that PERS staff made no misrepresentations to him but argued that it was unduly harsh to deny him early retirement benefits because he filed his paperwork three days late. The Board debated whether it could make an exception to NRS 286.541(2) and, if so, whether it would be allowing an in-service distribution and deviating from operational guidelines, which could jeopardize PERS with the IRS.

The Board denied Judge Smith's appeal in its written findings of fact, conclusions of law, and decision. It held that "[t]he applicable provisions of the Retirement Act [NRS 286.541(2)] clearly prohibit a member from retiring while he is actively employed and receiving service credit." Addressing Judge Smith's request for equitable relief, the Board first determined that NRS 286.190(3)(a) did not apply, since "Judge Smith could not point to any erroneous representation by [PERS] upon which he reasonably and detrimentally relied." Second, the Board concluded that "allowing a `retired' member to be employed and accrue service credit, with no clear break from service, violates the Internal Revenue Service's `in service distribution' rule and could jeopardize the entire retirement fund[']s status as a qualified retirement plan."

Under NRS 1A.280(3)(a), Judge Smith had until March 31, 2009, to give written notice that he intended to withdraw from PERS and participate in JRS. See supra note 2. If he did not, he would automatically remain in PERS. NRS 1A.280(5). Judge Smith signed and faxed his JRS election form on March 31. The form states, "I, Douglas E. Smith, hereby elect to withdraw from the Public Employees' Retirement System (PERS) and become a member of the Judicial Retirement System (JRS) pursuant to NRS 1A.280. I understand that this election is irrevocable and that I may not reestablish my service in PERS under any circumstances." Judge Smith transmitted the election form under a letter stating that he was doing so "under protest as there is an open appeal process on going." Pursuant to Judge Smith's election, PERS calculated its retirement benefits liability to him at more than $1 million. On June 15, 2009, PERS transferred that sum to JRS, which has invested and managed it since. The PERS Board's denial of Judge Smith's retirement application has not cost Judge Smith a loss of creditable service or any associated benefits.

Judge Smith petitioned for judicial review. After discovery, he and PERS stipulated to submit the dispute to the district court on the depositions taken and documents produced during discovery and the PERS Board hearing transcript and record. The district court thereafter entered its written findings of fact, conclusions of law, and order. It reversed the PERS Board's decision to deny Judge Smith's retirement application, declared a retroactive retirement date of January 8, 2009, and ordered PERS to pay all retirement payments due retroactive to January 8, 2009. PERS timely appealed.

II.

A.

Although not subject to the Administrative Procedure Act, "[t]he decisions of the PERS Board are reviewable by the courts on the basis of the same standard of review applied to other administrative actions." State ex rel. Dep't of Transp. v. Pub. Emps.' Ret. Sys., 120 Nev. 19, 23, 83 P.3d 815, 817 (2004). The court may not "`substitute its judgment of the evidence for that of the administrative agency.'" Id. (quoting United Exposition Serv. Co. v. SIIS, 109 Nev. 421, 423, 851 P.2d 423, 424 (1993)). "When the factual findings of the administrative agency are supported by [substantial] evidence, they are conclusive, and the district court is limited to a determination of whether the agency acted arbitrarily or capriciously." Mishler v. Nev. Bd. of Med. Exam'rs, 109 Nev. 287, 292, 849 P.2d 291, 294 (1993). "Substantial evidence is evidence which a reasonable mind might accept as adequate to support a conclusion." Schepcoff v. State Indus. Ins. Sys., 109 Nev. 322, 325, 849 P.2d 271, 273 (1993).

On appeal, this court "reviews questions of statutory construction and the district court's legal conclusions de novo." I. Cox Constr. Co. v. CH2 Invs., L.L.C., 129 Nev.___,___, 296 P.3d 1202, 1203 (2013). "However, an administrative agency charged with the duty of administering an act is impliedly clothed with the power to construe the relevant laws and set necessary precedent to administrative action, and the construction placed on a statute by the agency charged with the duty of administering it is entitled to deference." Elliot v. Resnick, 114 Nev. 25, 32 n. 1, 952 P.2d 961, 966 n. 1 (1998). "[W]hen an agency's conclusions of law are closely related to its view of the facts, those conclusions are entitled to deference, and we will not disturb them if they are supported by substantial evidence." Fathers & Sons & A Daughter Too v. Transp. Servs. Auth., 124 Nev. 254, 259, 182 P.3d 100, 104 (2008).

B.

NRS 286.541(2) defines when a PERS member's retirement becomes effective. It reads in its entirety:

To retire from PERS, NRS 286.541(1) requires the member to file a completed application for service retirement allowances with PERS. NRS 286.541(2) defines the effective date of retirement from PERS. It is the later of the four listed conditions. It can be the day after the employee's last day of employment, if the other three conditions have been met. NRS 286.541(2)(a). It can be the day the completed application form is filed with PERS, if the other three conditions have been met. NRS 286.541(2)(b). It can be the day after the employee's last day of creditable service, if the other conditions have occurred. NRS 286.541(2)(c). Or it can be the effective date specified on the application, again if the other three conditions have been satisfied. NRS 286.541(2)(d). Even if an employee has met all the other conditions of NRS 286.541(2), paragraphs (a) and (c) preclude that employee from effectively retiring until the day after the employee's last day of creditable service, whichever is later. Together, paragraphs (a) and (c) thus prevent an in-service distribution.

But the district court held that NRS 286.541(2) sets a retirement date only for purposes of calculating benefits, thus allowing Judge Smith to retire from PERS even after going to work for a PERS-eligible employer. It reasoned that the statute is codified in the benefits section of NRS Chapter 286 and that PERS's retirement application states retirement benefits are effective on whichever event listed in NRS 286.541(2)(a)-(d) occurs last. This interpretation is surely wrong. It contradicts the plain language of the statute, and "[w]ords may not be supplied in a statute where the statute is intelligible." 2A Norman J. Singer & J.D. Shambie Singer, Statutes and Statutory Construction § 47:38 (7th ed.2007).

Here, the statute conveys in no uncertain terms that retirement from PERS becomes effective when the last of the four specified events occurs. The statute does not establish a retirement date for a limited purpose, and it never uses the word "benefits." Although the district court is correct that NRS 286.541(2) is codified in the benefits section of Chapter 286, the statute defines eligibility to receive benefits. It would not make sense if NRS 286.541(2) applied solely to calculating benefits because other sections, such as NRS 286.495 and NRS 286.510, explain credit for service and how a member's designated retirement date affects his or her benefits. But there is no other statute that defines what conditions must be met before a member can effectively retire.

"While not controlling, an agency's interpretation of a statute is persuasive," State v. Morros, 104 Nev. 709, 713, 766 P.2d 263, 266 (1988), when the statute is one the agency administers. Elliot, 114 Nev. at 32 n. 1, 952 P.2d at 966 n. 1. The PERS Board governs PERS. See NRS 286.120. It has interpreted NRS 286.541(2) so as to comport with the statute's language and PERS's overarching obligation to comply with the Internal Revenue Service provisions applicable to governmental retirement plans. PERS indicates in its Preretirement Guide and its briefs that it does not limit NRS 286.541 to the calculation of benefits. Instead, PERS determines a member's effective retirement date based on information the member provides and which of the four events listed in NRS 286.541(2) occurs last. Thus, we conclude that an employee cannot effectively retire from PERS until the day when the last of the four enumerated requirements is complete.

C.

Here, Judge Smith remained an active PERS member until March 31, 2009, when he elected to transfer to JRS. The Board decided that the earliest Judge Smith could have effectively retired would have been January 8, 2009, "[t]he day the completed application form [was] filed with the System." NRS 286.541(2)(b). But because Judge Smith took his elected office on January 5, 2009, PERS received the application while he was employed in a PERS-eligible job. Under paragraphs (a) and (c) of NRS 286.541(2), a member still employed in a PERS-eligible job may not receive retirement benefits. After all, a person who continues PERS-eligible employment has not yet reached an effective "last day of employment" or "last day of creditable service." NRS 286.541(2)(a), (c).

Judge Smith's JRS election further complicates matters since he no longer has a PERS account from which he could draw benefits; all PERS contributions and liabilities have been transferred to JRS. The district court held that Judge Smith could revoke his JRS election because "[h]is hand was essentially forced." We recognize that Judge Smith's dispute with the PERS Board affected his decision to join JRS, but NRS 1A.280 plainly does not allow an employee to revoke his decision. Pursuant to NRS 1A.280(6), a judge who exercises the option to switch from PERS to JRS "may not re-establish the service for which the liabilities were transferred." Accordingly, after the Board transferred Judge Smith's accrued benefits from his PERS account to his new JRS account, he can no longer participate in or receive benefits from PERS.

III.

Judge Smith next argues that, even assuming his failure to retire from PERS before becoming a district court judge disqualified him from thereafter retiring and receiving benefits from PERS, the PERS Board should have granted him equitable relief under NRS 286.190(3)(a). This statute provides that the PERS Board:

NRS 286.190(3)(a) (emphasis added). NRS 286.190(4) defines "error or inequity" as "the existence of extenuating circumstances, including, but not limited to, a member's reasonable and detrimental reliance on representations made by the System or by the public employer pursuant to NRS 286.288 which prove to be erroneous, or the mental incapacity of the member."

Citing NRS 286.190(3), the district court held that the Board was required to grant Judge Smith equitable relief. But this reading ignores the statute's use of the permissive "may." "It is a well-settled principle of statutory construction that statutes using the word `may' are generally directory and permissive in nature, while those that employ the term `shall' are presumptively mandatory." Nev. Comm'n on Ethics v. JMA/Lucchesi, 110 Nev. 1, 9-10, 866 P.2d 297, 302 (1994). The district court's reading contravenes the presumption that every word, phrase, and provision — here, the word "may" — in a statute has meaning. Law Offices of Barry Levinson, P.C. v. Milko, 124 Nev. 355, 366-67, 184 P.3d 378, 386-87 (2008); In re Prosole, 32 Nev. 378, 383, 108 P. 630, 632-33 (1910).

"A statute's express definition of a term controls the construction of that term no matter where the term appears in the statute," so NRS 286.190(4)'s definition of "error or inequity" controls. Williams v. Clark Cnty. Dist. Attorney, 118 Nev. 473, 485, 50 P.3d 536, 544 (2002); 1A Norman J. Singer, Statutes and Statutory Construction § 20:8 (6th ed.2002). Under NRS 286.190(4), error or inequity signifies extenuating circumstances, such as detrimental reliance or mental incapacity of the member. Although its use of "including, but not limited to" makes NRS 286.190(4)'s list of extenuating circumstances nonexhaustive, it is significant that none of the examples involves employee fault or neglect.

Judge Smith and our dissenting colleagues cite Nevada Public Employees Retirement Board v. Byrne, 96 Nev. 276, 607 P.2d 1351 (1980), arguing that "our courts have the inherent power to seek and to do equity." This is a true statement but the circumstances in Byrne were much different from Judge Smith's. In Byrne, PERS incorrectly told an employee he would receive $725.35 a month upon retirement, but when the employee retired, he received a mere $86.78 a month. Id. at 278, 607 P.2d at 1352. Here, PERS gave Judge Smith accurate "Estimated Calculations" every time he requested information about his retirement options. Unlike Byrne, nothing suggests that the Board falsely or incorrectly recorded Judge Smith's information or gave him inaccurate information on which he detrimentally relied. In fact, as the Board noted, Judge Smith acknowledged that PERS staff made no misrepresentations. It appears that he chose to delay sending his retirement notice so as to ensure no gap in health insurance coverage as he changed jobs; this was his choice, not one PERS recommended. Judge Smith admitted that he did not read the materials PERS provided him. He failed to file his PERS retirement application before January 5, 2009, because he assumed that timing did not matter. Judge Smith relied on his own assumptions to his detriment.

The dissent would remand this matter back to the PERS Board with instructions "to make specific findings of fact and conclusions of law under its equitable powers set forth in NRS 286.190(3)." But the PERS Board has already done so. Thus, its written findings of fact, conclusions of law, and decision consider and reject application of Byrne because in Byrne, unlike this case, PERS made the error in calculation, on which the employee relied to his detriment. In this case, by contrast, the Board found that Judge Smith "has not alleged any error in his records, or the calculation or amount of his benefit." He asks "the Board [to] change the `effective date of his retirement.'" This the Board declined to do, because it would "violate[] the Internal Revenue Service's `in service distribution' rule and could jeopardize the entire retirement fund[']s status as a qualified retirement plan."6

NRS 286.190(3)(a) permits the Board to "[a]djust the service or correct the records" of a member or retired employee after "an error or inequity has been determined." By definition, "adjust" means to bring something into a proper state, and "correct" is to make something true, accurate, or right. Concise Oxford English Dictionary 16, 321 (11th ed.2008). But as the Board found, its records and calculation of Judge Smith's service were accurate. What Judge Smith sought was to have the Board rewrite its records to establish an earlier retirement date than the true record and application of NRS 286.541(2) would dictate. According to the Board, this placed the plan as a whole at risk, because it amounted to an improper in-service distribution. Such calculated risk avoidance — involving a subject within the expertise of the Board, not the courts — is something a court should not lightly second guess. See In re State Eng'r Ruling 5823, 128 Nev. ___, ___, 277 P.3d 449, 453 (2012). Under these circumstances, we cannot conclude that the PERS Board abused its discretion when it determined that Judge Smith must wait until he retires from his current employment to collect his service benefit, none of which he has lost by reason of the Board's determination in this case.

We therefore reverse.

We concur: HARDESTY, PARRAGUIRRE, and DOUGLAS, JJ.

GIBBONS, J., with whom CHERRY and SAITTA, JJ., agree, concurring in part and dissenting in part:

While I concur with the majority that NRS 286.541(2) determines the effective date of retirement, I disagree that the Board may not grant equitable relief pursuant to NRS 286.190(3) and (4).

As a deputy public defender, as a deputy district attorney, and as an elected justice of the peace, Judge Smith was required to be enrolled as a member of PERS. In 2001, the Legislature created the Judicial Retirement System (JRS) for supreme court justices and district judges. In 2005, the Legislature adopted NRS 1A.285 to allow a justice of the peace or municipal judge to participate in JRS.

The district court found that, after his election to the Eighth Judicial District Court in November 2008, Judge Smith advised PERS that he intended to retire from PERS prior to taking office as a district judge on January 5, 2009. Judge Smith would then become a member of the JRS on that date.

PERS sent the necessary paperwork to Judge Smith to complete for his retirement. The district court found that Judge Smith retired as a justice of the peace on December 31, 2008, and Judge Smith ceased having contributions made to PERS on his behalf as of that date. As set forth in the majority, PERS received Judge Smith's retirement application on January 8, 2009, or three days after he commenced his service as an elected district judge.

NRS 286.190 sets forth the general powers of the PERS Board. NRS 286.190(3)(a) provides in part that the Board "may adjust the service or correct the records, allowance or benefits of any member, retired employee or beneficiary after an error or inequity has been determined...." NRS 286.190(4) defines error or inequity as "the existence of extenuating circumstances, including, but not limited to, a member's reasonable and detrimental reliance on representations made by the System." Contrary to the majority's conclusion, this statute does not limit the Board's authority to grant equitable relief to PERS members who make inadvertent mistakes. After he retired on December 31, 2008, Judge Smith should have delivered his fully executed retirement application to PERS prior to January 5, 2009. The application required a notarized signature by Judge Smith's wife consenting to the terms of his retirement option. There was a delay in obtaining this notarization.

In Nevada Public Employees Retirement Board v. Byrne, 96 Nev. 276, 607 P.2d 1351 (1980), we affirmed the judgment of the district court estopping the PERS Board from altering the amount and calculation of retirement benefits it had originally represented to Mr. Byrne and ordering the payment of those retirement benefits. The PERS Board argued in part that because it had the inherent power to correct mistakes, any reliance on its representations was barred. Id. at 279, 607 P.2d at 1353. We disagreed and concluded that our courts have the "inherent power to seek and to do equity." Id. at 280, 607 P.2d at 1354.

In the present case, the district court found and determined that "PERS is equitably estopped from denying Judge Smith his PERS retirement benefits." The district court found and concluded that in response to reasonable inquires made by Judge Smith, PERS "at no time informed [Judge Smith] of a deadline for submitting his application. Neither was this deadline explained in the application packet or the applicable statutes." The district court further found and concluded that Judge Smith enrolled in JRS only because of the unresolved status of this litigation. Finally, the district court noted that the enrollment was made under protest and was hardly voluntary. Based on these findings and conclusions, the district court properly determined that the Board could not fairly deny benefits and thus should have turned to its own powers under NRS 286.190 to do equity.

Therefore, I dissent from the majority's stringent interpretation of NRS 286.190(3) and (4). The PERS Board does have the power to remedy an "error or inequity" based upon a mistake of the PERS retirement applicant. Otherwise, a minor error may reduce significant retirement benefits which the applicant has earned over many years of service. The PERS Board has the equitable power to rescind the enrollment by Judge Smith in the JRS. Since we do not make factual findings, I would reverse the judgment of the district court with instructions to remand this case to the PERS Board to make specific findings of fact and conclusions of law under its equitable powers set forth in NRS 286.190(3) and (4) regarding the extenuating circumstances in this case.

We concur: CHERRY, and SAITTA, JJ.