We haven't discussed the differences between de-rated thrust and assumed temperature method.
De-rate is a fixed thrust setting. Eg. T/O, rating 1 and rating 2 thrust levels.
That means if you use a de-rated thrust such as rating 1 or 2, it is almost like strapping on a smaller engine. You then have associated limits for that thrust rating e.g V speeds and maximum thrust.
Some airlines use de-rated T/O, but almost all use de-rate for the climb.
Assumed temperature method (ATM) is a thrust reduction based on not needing a full thrust T/O. Again you trick the engine into thinking that the outside air temperature is hotter than it really is. Therefore you have a lower thrust.
ATM can also be used with de-rates.
People sometimes use de-rate when they acutally mean ATM. Big difference!