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Leopold's not asking if you can move, attack, and move again.
He wanted to know if a character with only one attack needed a full attack action in order to use it.
The answer, as the others stated, is no. A full attack action is only required when making more than one attack.
Note, though, that a level 3 monk, with only one attack, would need to use a full attack in order to make use of his flurry. And the same for any other circumstance that allows multiple attacks.