A motion for rehearing is a prerequisite to judicial review. A motion for rehearing must be filed with the director within 20 days after the date of rendition of a final decision or order. Replies to a motion for rehearing must be filed with the system within 20 days after the date of the motion for rehearing, and system action on the motion must be taken within 60 days after the date of rendition of the final decision or order. If system action is not taken within the 60-day period, the motion for rehearing is overruled by operation of law 60 days after the date of rendition of the final decision or order. The director may by written order entered prior to the expiration of the 60-day period extend the period of time for taking system action, except that an extension may not extend the period for system action beyond 90 days after the date of rendition of the final decision or order. In the event of an extension, the motion for rehearing is overruled by operation of law on the date fixed by the order or, in the absence of a fixed date, 90 days after the date of the final decision or order. The parties may by agreement, with the approval of the director, provide for a modification of the time provided in this section.