When an appeal by the state is authorized by Florida Rule of Appellate Procedure 9.140, or sections 924.07 or 924.071, Florida Statutes, the state may file a motion for rehearing within 10 days of an order subject to appellate review. A motion for rehearing shall state with particularity the points of law or fact that, in the opinion of the state, the court has overlooked or misapprehended in its decision, and shall not present issues not previously raised in the proceeding. A response may be filed within 10 days of service of the motion. The trial court‘s order disposing of the motion for rehearing shall be filed within 15 days of the response but not later than 40 days from the date of the order of which rehearing is sought. If no order is filed within 40 days, the motion is deemed denied. A timely filed motion for rehearing shall toll rendition of the order subject to appellate review and the order shall be deemed rendered 40 days from the order of which rehearing is sought, or upon the filing of a written order denying the motion for rehearing, whichever is earlier. This rule shall not apply to post-conviction proceedings pursuant to rule 3.800(a), 3.850, 3.851, or 3.853. Nothing in this rule precludes the trial court from exercising its inherent authority to reconsider a ruling while the court has jurisdiction of the case.