pixel_player_195440103 this puzzle is one of the toughest! I really liked it. Here is how I solved it.
Make a key for yourself such as R for right, D for down, U for up. And have L for left just in case. (Of course, it depends whether you call the movement Left or Right - that is why I say make it a system that works for you. )Then as you discover each correct step, make a note on your paper. You'll get a list like R R D R U R R D R D etc. That isn't the solution btw, just an example.
You won't be able to remember them without it. Doing that made it possible to quickly get back to when I made an error and stepped on the wrong spot, closing the door.