landscaping around pool that soaks up rain water

[rodman82]

First year we put in our 24 foot above ground so with all of the digging, poor drainage for the rain water and new Yorks soil the rain does not have anywhere to go but around our pool. Muddy mess!!! We have put all soil back around pool but the soil is actually clay so it's not soaking it up like it should. You step in it you sink like quick sand.
I'm looking for landscaping ideas that will help this issue and look good. Rocks? Sand? I'm clueless. Thanks in advance

 

[Readyforapool]

Could you put in a drainage system that would carry the water away! Maybe a French drain or channel drain type?