Can a Dazed character use an Action Point?

[HighTemplar]

Pushing your heroic ability when the villain thought he'd taken you out of the round? Surprising him, and your team, by being extra cool?
I'd allow it. But I like cool.

What about "Pushing the villain's ability when the heroe thought he'd taken him out of the round? Surprising you, and his team, by being extra cool?"