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If I sell a call option (american option, covered call) on a stock and collect the premium, what happens if I then buy to close

If I sell a call option (american option, covered call) on a stock and collect the premium, what happens if I then buy to close for that same option (same strike and expiration) for a profit? Is assigmnent still possible here (someone exercises the option I sold them and I exercise the option I bought), or would I be able to do another covered call (at a later expiration) without having to worry about assignment/exercising the option? Sorry about the bad wording.

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