How can I climb the rainbow?

Hint 1 of 4:

You can't do it from inside, because you're not allowed to put anything on
the floor to help you climb up.

Hint 2 of 4:

And you can't take anything out of the room, so you'll have to rely on
what's available outside of the cabin.

Hint 3 of 4:

Keep clicking long enough, and you should find a familiar item.

Hint 4 of 4:

Something you've used before for climbing.