OAT plus INVERSION TEMP = Temp used for takeoff calculation.
If using FLEX/ASS then you will have lower temperature.
If using TOGA, then you will have a weight reduction........
Not many airlines use inversion temperatures due to the weight loss
With flex you can run the thrust back up to the (relevant) derate or max thrust setting but, I suggest, slowly to avoid any nasty surprises.
...... gotta disagree, you cannot run it back to max thrust due to lack of VMCG protection......
Mutt