As used in this Charter, "agency" means any department, division, bureau, board or commission in the administrative branch of the City government. As used in this section, "reorganize" or "reorganization" shall mean the abolition, consolidation, or modification of existing agencies, or the creation of new agencies. No agency of the City may be reorganized except in the manner provided in this section. The exclusive power to initiate a reorganization of an agency of the City shall be vested in the Mayor. The Mayor may propose a reorganization by filing a copy of the proposed ordinance or resolution setting forth the detailed provisions of the reorganization with the Clerk of Council. The Council shall consider the proposed ordinance or resolution setting forth the proposed reorganization in the same manner as any other ordinance or resolution, except that if it is modified or amended by the Council in any way it shall not be voted on as to its passage unless the Mayor shall agree to the modification or amendments in writing. If the Council fails to act upon an ordinance or resolution proposing a reorganization within 60 days after it is filed with the Clerk of Council, such ordinance or resolution shall be deemed to have been rejected and the power of the Council to adopt it shall lapse. The Mayor may reinitiate the proposed reorganization, or a modification thereof.