It shall be the duty of the retirement board to:
(1) Determine the eligibility of an individual to be a member of the retirement system and other questions of fact in the event of dispute between an individual and a department;
(2) Adopt rules and regulations, as the board may deem necessary, for the management of the board;
(3) Prescribe the form in which employers report contributions, hours worked by school employees, payroll information, and other information necessary to carry out the board's duties;
(4) Keep a complete record of all proceedings taken at any meeting of the board;
(5) Employ a director and such assistants and employees as may be necessary in the performance of its duties; and
(6) Obtain actuarial services pursuant to subdivision (2)(e) of section 84-1503.