The Mayor shall have power to veto or sign any ordinance passed by the City Council; provided, that any ordinance vetoed by the Mayor may be passed over his/her veto by a vote of one-half (1/2) plus one (1) of the members of the Council elected, notwithstanding the veto, and should the Mayor neglect or refuse to sign any ordinances and return the same with his/her objection, in writing, at the next regular meeting of the Council, the same shall become a law without his signature. (1988 Code)