First, go to the end of the track on the floor, where you'll find the power core inside a rolling cage. Use the magnetic grapple to pull it along until it runs up against a bit of debris blocking the track.
Climb onto the cage and jump to grab the ladder. Climb up and jump to the right to the broken metal ledge.
Amanda cuts in over the headset to quiz Lara on her knowledge of Arthurian lore. (This short cinematic is called "Headset Highjack".)
Carefully jump from the bent edge of the ledge to grab the horizontal bar. Swing around and jump to the next ledge. Jump to grab the dangling rope.
Swing and jump to grab the contraption with the big, blue ball hanging from the ceiling.
Climb around to the far side of the contraption. Jump back to grab the next horizontal bar.
Swing around and jump to the ledge against the far wall. Turn right, carefully move to the broken edge and jump to grab the ladder against the wall.
The ladder extends to the floor, so if Lara falls after this, you can climb up here. Climb the ladder and jump to the ledge on the right.
Shoot the fuel barrel behind the barred window to break the bars.
Then take a running jump off the bent part of the ledge to grab the dangling rope. Adjust Lara's angle and climb up the rope a bit if necessary. If you swing while hanging too low on the rope, Lara bangs into the ledge behind her and falls. Swing and jump into the control room.
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