Absent a properly noticed written motion for continuance under Rule 231 or for voluntary dismissal under section 2-1009 of the Code of Civil Procedure (735 ILCS 5/2-1009), a motion for continuance or voluntary dismissal made on the date of trial shall be denied, and the case shall proceed to trial, unless:
(a) The court finds that (i) each party has consented to a continuance with an understanding of the potential consequences of not consenting and (ii) a continuance serves the interest of justice; or
(b) The court is unable to proceed on the trial date, in which case an order may be entered continuing the case for a final trial date.
(c) Nothing herein shall limit the right of any litigant to seek a continuance subject the provisions and requirements of Rule 231(f).