The ruling on the prayer of one who bowed while the imam had prostrated for the prostration of recitation

Question:
He says: Honorable Shaykh, may Allah grant you success. A man was praying behind the imam, and the imam recited a verse of prostration and prostrated. The ma'mum thought the imam had bowed, so the ma'mum bowed. When the imam raised his head from the prostration, the ma'mum realized that it had not been a bowing. What does he do in this situation?

Answer:
He owes nothing; his prayer is valid because he left a recommended practice. He did not leave an obligatory act, he did not leave an obligatory act or a pillar of the prayer; rather, he left a recommended practice, so his prayer is valid. Yes.