kitchen P-Trap clogged on 2000LXI

[luckyron1]

Drano Max worked for awhile. Now it stops up after just a couple cups
of water. I dissassembled the easy screw off stuff and ran a 7$ Home
Depot plumbing snake/tape down it but couldn't get past the trap. I've
never done this kind of thing before and maybe I'm being a little over-
cautious. The vertical pipe to the trap is poly. Unfortunately, due
to cabinetry obstructions, I can't see to the trap so I don't know what
kind of trap I'm dealing with. I'm afraid that it might also be poly
and I don't want to risk breaking it should I use too much force.
Theres almost no access from above it and due to the fact that it's in
the slide there's no way to get to it from underneath that I can see
anyway. Anybody done this before?
Thanks guys and Happy Holidays!!

Ron & Ruth in San Antonio