The first meeting of the council in each year shall be held on the first Wednesday after the first Monday of January at noon. All meetings of the council shall be held as provided by its rules; provided, however, that at least two stated meetings shall be held each month, except in its discretion in July and August. A majority of the council members shall constitute a quorum. At least thirty-six hours prior to a stated meeting of the council, or as soon as practicable prior to a special meeting, the council shall publish and make publicly available a proposed agenda for such meeting, including a list of all proposed local laws or resolutions to be considered at such meetings.