A group I'm with is using the healing custom power. It doesn't specify what kind of action it is. You may want to clarify this:
HEALING [-2] Description: You possess the magical ability to heal others. Perhaps you can help people recover from psychological trauma with your musical genius, or perhaps you can knit flesh and bone back together through sheer faith. Note: This power uses one skill and applies to one stress track. Choose which skill and which stress track when you take this power. Any combination is permissible as long as the group is not offended by it. Skills Affected: Pick one. Effects: Heal. You may use your chosen skill to heal consequences of your chosen stress track. In order to heal a given consequence, you must exceed its shift value on a roll of your chosen skill. Healing a consequence increases the speed of its recovery by one step, or by two steps if your roll is twice as good as it needs to be, or by three steps if by some miracle your roll is three times better than it needs to be. If an attempt is made to heal a consequence that has already been healed, the second attempt replaces the first. This power may or may not affect extreme consequences; GMs should handle such issues on a case by case basis.
Given the fact that you can re-roll a, seemingly unlimited, amount of times and take the best roll, it might be good to know what kind of action it is.
It also doesn't specify whether it allows you to instantly heal mild consequences. I'd assume, if you do it "twice as fast" it moves it from "after the next scene" down to "at the end of the current scene" and then down to "immediately in this exchange" (as per the recovery power.)