Your question is covered by Florida Rule of Civil Procedure 1.420(e), which provides as follows:
"(e) Failure to Prosecute. In all actions in which it appears on the face of the record that no activity by filing of pleadings, order of court, or otherwise has occurred for a period of 10 months, and no order staying the action has been issued nor stipulation for stay approved by the court, any interested person, whether a party to the action or not, the court, or the clerk of the court may serve notice to all parties that no such activity has occurred. If no such record activity has occurred within the 10 months immediately preceding the service of such notice, and no record activity occurs within the 60 days immediately following the service of such notice, and if no stay was issued or approved prior to the expiration of such 60-day period, the action shall be dismissed by the court on its own motion or on the motion of any interested person, whether a party to the action or not, after reasonable notice to the parties, unless a party shows good cause in writing at least 5 days before the hearing on the motion why the action should remain pending. Mere inaction for a period of less than 1 year shall not be sufficient cause for dismissal for failure to prosecute."