Rule book (pg8):
You can use your quickcast action at three times during the Action Stage:
• During the First Quickcast Phase
• Immediately before or after any creature you control takes its Action Phase
• During the Final Quickcast Phase
When it is your turn to take an Action Phase, you must activate one of your active creatures. However, if your opponent has more active creatures in the arena than you have, you may choose to pass when it is your turn to take an Action Phase.
Rule book (pg9):
When you choose a creature to take an Action Phase, you activate it. You must flip over the creature’s action marker to the inactive side, and you must discard any guard marker (if it has one). Then your creature may take its actions for the round (see “What Can A Creature Do” on page 11).
Note: As soon as you activate a creature and flip its action marker, your opponent can reveal any hidden enchantments
(see “Revealing Enchantments” on page 18). You must give your opponent a chance to reveal his enchantments before
you decide which action you want to take with your creature.
Remember that before you activate a creature (including your Mage), or immediately after you have completed its Action Phase, you can use your quickcast action (if your quickcast marker is active).
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In my understanding we can break it down as follows:
#1. Choose to take actions or pass
#2. Opportunity to use your Quickcast Action
#3. Activate a creature (flip the action marker)
#4. Ask opponents if they want to reveal enchantments (you can also reveal your own enchantments)
#5. Carry on your action phase
Therefore, you can choose the creature after resolving your quickcast, but you cannot pass if you used your quickcast.