Members and third-party payees may appeal any decision made by the system that affects their rights under this chapter. The appeal shall be filed with the system within thirty days after the notification of the decision was mailed to the party’s last known mailing address, or the decision of the system is final. If the party appeals the decision of the system, the system shall conduct an internal review of the decision and the chief executive officer shall notify the individual who has filed the appeal in writing of the system’s decision. The individual who has filed the appeal may file an appeal of the system’s final decision with the system under chapter 17A by notifying the system of the appeal in writing within thirty days after the notification of its final decision was mailed to the party’s last known mailing address. Once notified, the system shall forward the appeal to the department of inspections and appeals.