Power of All & canceling action cards / equipment

Hello,
Power of All lacks the text 'no cost is paid', so it can be source of nice pool damage if you manage to target an expensive master card like Zillah's Valley. What about canceling action cards/equipment, lets say Assault Rifle?
The way we have played it so far is that cost is not paid, because cost for action is normally only paid at successful resolution and Power of All is played at announce the action phase. Is this the correct way to handle the interaction?

Name: Power of All
[TR:C]
Cardtype: Reaction
Cost: 2 blood
Requires a ready anarch.
Tap this anarch and one other untapped ready anarch you control to cancel a
library card as it is played. Usable even if there is no action. Not usable
during your own turn.

Whisker wrote:

Hello,
Power of All lacks the text 'no cost is paid', so it can be source of nice pool damage if you manage to target an expensive master card like Zillah's Valley. What about canceling action cards/equipment, lets say Assault Rifle?
Is this the correct way to handle the interaction?.

For action cards where you don't pay until you reach action resolution, Power of All won't make you pay - the action never gets that far, having had the card cancelled.