a. Every local law certified by the clerk of the council, after its passage by the council, shall be presented to the mayor for approval.
b. If the mayor approves the local law, the mayor shall sign it and return it to the clerk; it shall then be deemed to have been adopted. If the mayor disapproves it, he or she shall return it to the clerk with his or her objections stated in writing and the clerk shall present the same with such objections to the council at its next regular meeting and such objections shall be entered in its journal. The council within thirty days thereafter may reconsider the same. If after such reconsideration the votes of two-thirds of all the council members be cast in favor of repassing such local law, it shall be deemed adopted, notwithstanding the objections of the mayor. Only one vote shall be had upon such reconsideration. The vote shall be taken by ayes and noes, which shall be entered in the journal. If within thirty days after the local law shall have been presented to him or her, the mayor shall neither approve nor return the local law to the clerk with his or her objections, it shall be deemed to have been adopted in like manner as if the mayor had signed it. At any time prior to the return of a local law by the mayor, the council may recall the same and reconsider its action thereon.