2 added 249 characters in body
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Your assumption is correct. Unlike, for example, Spiritual Weapon, Mage Hand doesn't say anything about a free use on the turn you cast it, so it requires your action to cast it followed by your action on a subsequent turn to use it.  

Minor caveat: An Arcane Trickster can control a Mage Hand with a bonus action, so they could create with their action then use it with their bonus action. Also, a Fighter could use Action Surge to gain an extra action and use it on the same turn.

Your assumption is correct. Unlike, for example, Spiritual Weapon, Mage Hand doesn't say anything about a free use on the turn you cast it, so it requires your action to cast it followed by your action on a subsequent turn to use it.  

Your assumption is correct. Unlike, for example, Spiritual Weapon, Mage Hand doesn't say anything about a free use on the turn you cast it, so it requires your action to cast it followed by your action on a subsequent turn to use it.

Minor caveat: An Arcane Trickster can control a Mage Hand with a bonus action, so they could create with their action then use it with their bonus action. Also, a Fighter could use Action Surge to gain an extra action and use it on the same turn.

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Your assumption is correct. Unlike, for example, Spiritual Weapon, Mage Hand doesn't say anything about a free use on the turn you cast it, so it requires your action to cast it followed by your action on a subsequent turn to use it.