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If I interpret your post correcty, you are long the stock, and bought June 2024 $360 puts to protect profits against a temporary drop. This could work if there indeed is a temporary drop, and you can close the long put at a profit and then ride the stock back up unhedged.
Long stock + long put = long call ... so your new position is the equivalent of a long June 2024 call. If the stock drops, you don't lose except some time value. If the stock zooms past $360 you start partaking in the profits again.
