Go to the far left corner of the courtyard.
At the top of the ramps is a closed door. Note its location. Then climb the ladder to the left.
Follow the passageway around...
...to an opening overlooking the COURTYARD. Pull the switch on the left side of this opening to open the door below, but don't drop down yet.
Turn around so the switch is on Lara's right and follow the passageway forward toward the blue gate. Before this gate, on the right, is another opening overlooking the COURTYARD.
Take a running jump from the opening to land on top of the tall, angled pillar.
Then take another running jump to grab the ledge with the save/power-up crystal and rocket. Pull up, get the goodies, and then safety drop to the floor.
NOTE: If you don't have the ROCKET LAUNCHER, you'll get it here instead of the rocket.
Now turn around and head for the far left corner again.
Hop up onto either of the angled ledges flanking the door you just opened. Then jump into the doorway.
Inside, in a little alcove on the right, you'll find the FIRST ULI KEY.
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