If I may add to Genghis's excellent brief, based on my own painful experience many years ago: first thing after EFATO, push the nose down and be prepared for a much steeper angle of descent because of absence of slipstream and the extra drag from the stationary prop. If I must turn, put the nose down even more and if one wing drops, use opposite rudder and put the nose down still further.
I was shocked to learn that PPLs are no longer required to demonstrate spinning and recovery. Yet all too often we see in AAIB witness reports: "I heard the engine stop, then the plane turned steeply and dived into the ground."