Temperature is just a measure of the average kinetic energy (motion) of the molecules in a gas. If you decrease the temperature, that means they’re moving slower.
If they’re moving slower, then they’re running into the walls of the syringe less often AND slower. This means they’re pushing less hard on the sides of the syringe. The outside air pressure is still pushing in equally hard, but the inside gas pushing out is less, so the outside air wins, and pushes inward. This is the volume decreasing.
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