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I am stuck in one room in the pyramid.

There are two big pillars, with two smaller pillars on top of each of them and a cauldron on one of the smaller pillars.  For of these pairs of pillars, there's a wheel that can raise one of them while lowering the other.   There are also wheels for rotating the two big pillars and for rotating the entire assembly.

I think that the only way to gain enough altitude to exit the room is to launch from a cauldron that is on a fully raised smaller pillar that is in turn on top of a fully raised big pillar.  I also think that the only way to gain enough altitude to reach such a pillar is to launch from the cauldron that's in one corner of the room on its own pillar, separate from the rotatable assembly that fills most of the room.  So I need to make a two-stage flight, from cauldron 1 (in the corner) to cauldron 2 (on the stacked raised pillars) to the exit.

My problem is that I can't seem to get enough horizontal flight distance to get from that cauldron to the other cauldron to the exit.  Cauldron 1 is immobile, and no matter how I position cauldron 2, it's either too far away from cauldron 1 for the first stage of my flight or too far away from the exit for the second stage.

I've been stuck on this puzzle for days now, which is annoying because there's no bonfire anywhere near the puzzle.  I can't find any online walkthroughs for this game either.  Is there a flaw in my analysis?  Do I just need to position cauldron 2 more precisely?  Do I need some sort of power-up for this puzzle?  Or is this puzzle unsolvable?