(1) Filing; service. A petition for reopening the hearing to take further evidence, or for rehearing or reargument of the proceeding, or for reconsideration of the order shall be made by petition addressed to the Secretary and filed with the hearing clerk, who immediately shall notify and serve a copy thereof upon the other party to the proceeding. Every such petition shall state specifically the grounds relied upon.

(2) Petitions to reopen hearings. A petition to reopen the hearing for the purpose of taking additional evidence may be filed at any time prior to the issuance of the final order. Every such petition shall state briefly the nature and purpose of the evidence to be adduced, shall show that such evidence is not merely cumulative, and shall set forth a good reason why such evidence was not adduced at the hearing.

(3) Petitions to rehear or reargue proceedings, or to reconsider orders. A petition to rehear or reargue the proceeding or to reconsider the final order shall be filed within 15 days after the date of the service of such order. Every such petition shall state specifically the matters claimed to have been erroneously decided, and alleged errors must be briefly stated.