I altered the wording of part of my piston Multi-Engined T/O brief after an experience I had once. Have you considered how you would identify an engine failure on take off? How would it present itself? What if it was a partial failure?
I was on board a C310 that had a partial engine failure on take off. The take off was attempted and aborted a couple of times before a decision was made to visit a LAME. What happened? Everything indicated and sounded perfectly normal taxiing around. With the levers fully forward and rolling down the (fortunately wide) runway the pilot was unable to keep the aircraft straight. With full opposite rudder the aircraft veered off to one side.
LAME's investigation found crud had entered the fuel system (probably while the aircraft had been sitting stripped in the open waiting for a paint job). Injectors were blocked and the offending engine was effectively firing on 3 out of 6 cylinders. If the engine had been run for much longer engine damage probably would have followed rather rapidly. I was just glad it hadn't happened on the previous take off when I was flying and taking off on a narrow, downhill, shorter island strip where an aborted take off would have still been the right thing to do but would have resulted in a different outcome.
From that observational experience I changed the first part of my brief to: "If I have a major directional control problem on take off below (decision speed/blue line) I'll treat it like an engine failure, control the aircraft with rudder, close both throttles and pull up/land on the remaining runway."
The brief definitely has to be a 'thinking' process. However as a student, the best thing you can do is sit down and write up the brief for yourself with the possible variables. Memorize it and go and sit in the aeroplane (last time I checked, it doesn't cost you a cent to hop in a plane and sit in it for a while on the ground - and it can save you some real dollars and make you a much better pilot). Go through the brief, touching the items as you call them. At the very least, close your eyes and visualise the process. They used to call it 'chair flying' - it works.
I still do that process when possible, especially when transitioning to new aircraft types. Remember the brief should take into account correct procedures out of the POH. For example, depending on what aircraft you are flying, the gear should be raised before the flap and the exact opposite in other types! Tailor the brief to the aircraft type and conditions you are in. Goodluck and stay safe!