Jake vs. Jack (Smiling Jack timing question)

You resolve the blood and pool effect from Smiling Jack during your untap phase in the order you wish, correct? Each one is an independent effect?
So you can burn a vamp's blood to 0, burn Jake Washington to get more blood, and continue burning blood and or pool for the rest of the Jack counters?

Or do you have to resolve all of the Jack counters both independently and all at once?