Before any board of trustees, common council, or other legislative body of any city, or the board of trustees of any library district gives notice that the city or library district desires to become a part of the county free library system, or gives notice of withdrawal from the system, the board of trustees, common council, or other legislative body of the city or the board of trustees of the library district shall publish at least once a week for two successive weeks prior to the giving of either notice, in a newspaper designated by the board of trustees, common council, or other legislative body of the city or the board of library trustees of the library district, and circulating throughout the city or library district, notice of the contemplated action, giving the date and the place of the meeting at which the contemplated action is proposed to be taken.