The contact area between your tires and the ground is equal to the load on the tire divided by the pressure in the tire.
If you have high pressure the tire will load up a small area of sand and then cut into it, and will then have ineffective contact with the surrounding sand making it hard to get traction – the actual load will still be transferred to a small area of sand.
If you lower the pressure the contact area gets much larger, so your tires cut into the sand less to start with and if they do they have more effective contact for getting traction to get out.
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