How do I get through the security gates?

Hint 1 of 9:

The gate system here is basically a complicated maze.

Hint 2 of 9:

You need to collect three black cards to get to the Pre-Approval room.

Hint 3 of 9:

Notice what happens whenever you walk into a different room here.

Hint 4 of 9:

You have to give up some of your security cards, but you get back cards of a
different color.