Light a flare before stepping out so you can see where you're going. The collapsing floor tiles are outlined in the screenshot above. Step out onto them.
Fall through onto the slope below.
Slide and grab the edge. Then drop onto the longer slope below.
As Lara slides, the camera shifts to show her coming down the slope.
It may help to tap the Look button to switch back to Lara's perspective. Jump over the blade and continue sliding.
At the end of the slope with the blade, just let Lara slide.
She'll drop onto another slope as a rolling boulder passes overhead.
When the brick chute ends and Lara lands on the wet, gray slope. . .
. . . press Jump and Roll so she lands facing uphill.
Continue sliding past a short drop-off. (You can grab and release to break Lara's fall here, but she won't take damage if you don't.)
Grab the edge at the end of the slope to stop Lara from dropping into the pool below.
Traverse to the left and pull up into an alcove where you'll find SECRET #1, the Gold Dragon.
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