The carpet of flying says:
You can speak the carpet's command word as an action to make the carpet hover and fly. It moves according to your spoken directions, provided you are within 30 feet of it.
If a creature is riding this carpet and leaves the reach of an enemy creature, do they provoke an opportunity attack from them? Specifically, does using an action to command the carpet to move (which then moves you) count as using your action to move for the purposes of provoking an opportunity attack?