The Retirement Commission shall employ the services of one or more actuaries, each of which shall be an individual or firm having on its staff a fellow of the society of actuaries, to carry out the actuarial duties of sections 5-156, 5-156a and subsection (b) of § 5-168 and for such related purposes as the Retirement Commission deems advisable. The cost of such services shall be charged to the retirement fund. The actuary shall make such investigations of the mortality, service and compensation experience of the members of the system as the commission shall recommend and authorize, and on the basis of the investigations he shall recommend for adoption by the commission such tables and rates as are required. Having regard to the investigations and recommendations, the commission shall adopt such tables as it deems necessary and shall certify the rates of contribution necessary to fund the system. At least once in each five-year period, the actuary shall make actuarial investigations into the mortality, service and compensation experience of the members and beneficiaries of the system and shall, at least once in each two-year period, make a valuation of the assets and liabilities of the funds of the system. The commission, taking into account the results of such investigations and valuations, shall adopt for the system mortality, service and other tables as it deems necessary and shall certify the rates of annual contribution payable under the applicable provisions of this chapter.