I have attached the applicable part of the rules of procedure. Yes you can amend without seeking leave of court.
Fla. R. Civ. P. Rule 1.190 (a) Amendments. A party may amend a pleading once as a matter of course at any time before a responsive pleading is served or, if the pleading is one to which no responsive pleading is permitted and the action has not been placed on the trial calendar, may so amend it at any time within 20 days after it is served. Otherwise a party may amend a pleading only by leave of court or by written consent of the adverse party. If a party files a motion to amend a pleading, the party shall attach the proposed amended pleading to the motion. Leave of court shall be given freely when justice so requires. A party shall plead in response to an amended pleading within 10 days after service of the amended pleading unless the court otherwise orders.
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