The adjudication of disputes between claimants of preference rights to tidelands, including adverse claims, shall be performed by the assembly. Upon receipt of the working files in all disputes from the clerk, the assembly, through the clerk, shall set the dispute for hearing and determination, and cause notice to be served on all parties. Upon the assembly’s having heard the dispute, it shall enter its ruling thereon as quickly as possible, but not later than 10 days after the matter has been heard. An aggrieved person shall have the right of appeal to the superior court in accordance with the Rules of Appellate Procedure of the Alaska Supreme Court.