Aviate-Navigate-Communicate is a meaningless platitude unless the "How" is addressed. It is like saying "Be A Better PIlot", sounds nice but it is not very helpful advice.
Lets take for example the tragic Tomahawk EFATO accident. In this case the engine failed but the climb attitude was maintained until the airplane stalled and spun.
So how do you train for the "aviate" part for this scenario. Well what I do is require all my ab initio students do a takeoff brief before every takeoff. The first thing on the brief is "wheel forward establish gliding attitude". While they are verbalizing this I get them to physically push the control wheel forward. My hope is that this will become an automatic reaction that will save their life in the event of an EFATO.
All of that is true. In both cases I cited the pilot allowed the speed to decay and the AoA to increase. They did not GET THE NOSE DOWN! Naturally, in each case the aeroplane stalled and spun.
Yet both those pilots got out a radio call, the one who died did so as the aeroplane was slowing and its AoA increasing (it isn't clear whether this was the case in Cranfield accident). That shows that not only did those pilots not do the intuitive thing and take care of AoA, they diverted attention to getting on the horn to talk to someone! Why? First... FLY THE AEROPLANE!
When it happened to me (ironically off that same runway the pilot died from) in the Chippy the first thing I did was to get the bleeding nose down - quite sharply. And I didn't have to think about it... many, many PFLs had made it instinctive! Only when the aeroplane was stable in (slow, slightly descending) flight did I get on the horn to warn everyone else to get out of the way as I was landing IMMEDIATLY off a very short final from a very low circuit (I coundn't hear the radio even though using a headset because of the cachophony from the mis-firing engine, so just put out repeated transmissions).
Aviate (get the AoA under control), navigate (pick your field), if there's time, communicate (warn other traffic what you are doing).