Project Atlas is a Corporation agenda that can be over-advanced to provide agenda counters for the following ability:
Hosted agenda counter: Search R&D for 1 card, reveal it, and add it to HQ. Shuffle R&D.
Because it has no [Click] requirement, I understand that I can use this ability during the Runner's turn.
Imagine that I have a scored Project Atlas with a counter on it and the Runner runs on HQ. They pass the last ICE. Before the Runner accesses HQ, can I use this ability to fetch (say) a Snare into my HQ?
If so, must I do it before they choose to access (so that they could see me add the card and then jack out without accessing)? Or can I do it after they confirm that they want to access a card, giving them no opportunity to jack out?