v [T]
to make changes to an idea, method, system etc in order to improve it or make it more modern
= reform
　plans to reinvent the American educational system
reinvent yourself
to do something differently from before, especially in order to improve or change the way people think of you
　Bowie has constantly reinvented himself during his long career.
reinvent the wheelinformal
to waste time trying to find a way to do something when someone else has already discovered the best way to do it