During such six-year period as aforesaid, the board shall make a continuing study of the functioning of the city government and may, by a two-thirds vote of its members, not less than four years after such charter shall have taken effect, require the submission to the qualified voters of the city of the question of whether the charter shall be revised as a whole, such submission to be in accordance with the pertinent provisions of article four of this chapter. In the event revision as a whole is voted pursuant to such submission, the board as then constituted shall proceed to prepare a revision of the charter as a whole and the process of revision as a whole as so initiated shall be the same as that for the framing and adoption of a charter under the pertinent provisions of said article four of this chapter. During such six-year period as aforesaid, by a two-thirds vote of its members, at any time not less than one year after such charter shall have taken effect, the board may require the submission of one or more proposed charter amendments to the qualified voters of the city, in accordance with the pertinent provisions of article four of this chapter.