Communicate, Navigate, Aviate
Pilots learn a thing very early on in their training. It's the phrase "aviate, navigate, communicate". It teaches them to focus first on flying the plane, then on where you're going, and last on communicating with Air Traffic Control. That makes a lot of sense - if you are prioritise communicating with ATC over keeping the plane in the air, you're not going to have a good time.
This order of operations is really hammered in, because in an emergency it becomes paramount to focus on the right things at the right time.
That made me wonder: how does that translate to dealing with incidents as an on-call engineer?
I think the order there should actually be the opposite. Spending a couple of minutes more communicating and thereby slowing down the actual recovery slightly is definitely a worthwhile thing. Tell your customers what's broken, talk to the team about what is happening. Create a plan of action and agree on it before executing (the "navigating"?), then go and execute (the "aviating"?).
The main difference about these two scenarios might be the context: the pilot is focussing on preventing a disaster, the on-call engineer is focussing on recovering from a disaster.
So, on-call engineers: communicate, navigate, aviate.
(doesn't quite have the same ring to it, though)