(a)   Any ordinance or resolution passed by council shall be signed by the presiding officer and presented to the mayor by the clerk of council. If the mayor approves the ordinance or resolution, the mayor shall sign it within 10 days after its passage or adoption.
   (b)   If the mayor does not approve an ordinance or resolution, the mayor shall return it to council with a statement of his or her objections to the measure within 10 days, or if council is not then in session, at the next regular meeting of council, which objections council shall enter into its minutes. The mayor may approve or disapprove the whole or any item or part of any ordinance or resolution appropriating money, but otherwise the approval or disapproval shall be addressed to the entire ordinance or resolution. Not later than at the next regular meeting, council shall reconsider the legislation and, if upon reconsideration the legislation or the part of the legislation disapproved by the mayor is approved by a vote of two thirds of all members of council, it shall then take effect as if it had received the signature of the mayor.
   (c)   If the mayor does not sign or disapprove an ordinance or resolution within 10 days after its passage, it shall take effect in the same manner as if the mayor had signed it on the 10th day.