It knows how to use your at-will abilities, somehow... it seems likely that it gives an order and you effectively go about it to the best of your abilities.
And yeah, my bad on Quickdraw. Something like battle harness armor would have been better.
At any rate, the 'only one action' camp is still saying that you'd deny the ability to talk while dominated, correct?
What about if the vampire, say, who was dominating used an ability that gave the dominated target a free action attack? Vampires often have classes, this is not so far-fetched actually.
When you usually get only one action (dazed) 'choose your action' is correct, but it's not binding to 'can only take one action', but dazed does not in fact limit you to only one action, so it seems unlikely the intent is that you can't take any other actions whatsoever. For example, a dominated character who moves through a zone of tar that has a rule 'As a free action at the start of your turn, make an Athletics or Acrobatics check to avoid being immobilized until the end of your turn' could presumably do so.