(a) Prior to the first regular meeting in July of each even numbered year, the Mayor-elect, the Council member-elect, and the Recorder-elect shall meet in special public session in the Council Chamber and shall be called to order by the incumbent Mayor or, in his or her absence, by the incumbent Recorder or, in the absence of both the incumbent Mayor and the incumbent Recorder, Council Member with longest tenure or Council Member-elect, whereupon those officers-elect who have not as yet taken the prescribed oath of office shall do so before an officer who is authorized by law to administer oaths, at which time they shall be deemed to have qualified for the office to which they, respectively, have been elected; provided, that no officer who is required to give bond shall be deemed to have qualified until such bond has been given, except for the specific purpose of participating and voting in this particular meeting and any adjourned session thereof.
(b) The City Council shall then proceed to adopt, readopt, or amend rules governing the official conduct of its members and the transaction of its business, and the failure to do so shall have the effect of continuing in force the rules of the preceding Council. The Council shall then proceed to consider and act upon other matters of an organizational nature such as filling vacancies in appointive offices which are within the appointive authority of the Council or of the Mayor and Council; but no such office shall be deemed vacant when it is in fact held by an incumbent unless the office be declared vacant by a majority vote of the Council.