In a sense, nothing does.
If I’m on a small boat and I walk north, the boat gets pushed south. On average by weight, while I move and the boat moves, the two combined don’t move at all.
There’s a sort of joke that, technically, a rocket never leaves the launch pad, because the average position of its exhaust gas and the rocket itself never moves.
Of course, things do still move, just not on their own. Every thing that moves is just accompanied by something else that moves in the opposite direction. When you walk on Earth, the planet is ever-so-slightly shifted by it.
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