The Archimandrite

You can’t gain negative amounts of life. If you have fewer than four cards in hand as the first ability resolves, you won’t gain any life, but you won’t lose any life either.

Since The Archimandrite’s activated ability doesn’t have a tap symbol in its cost, you can tap creatures that haven’t been under your control since your most recent turn began (including The Archimandrite itself) to pay the cost.