Business sessions of the annual town meeting shall be held on the first Monday in May and may be continued on such additional days as may be decided by the town meeting. There shall also be a second business session of the annual town meeting held in the last 3 months of the calendar year on a date to be determined by the select board that shall be an "annual town meeting" for purposes of the General Laws; provided, however, that the select board may, at its discretion, cancel said fall annual town meeting not later than September 15 in any year, so long as not more than 10 petitioned articles have been submitted for inclusion on the warrant at said fall annual town meeting and notice of the board's action with regard to such meeting shall be posted on the town's website and principal bulletin board. The board's decision as to whether to hold a fall town meeting shall not prohibit the board from calling for a special town meeting at its discretion.