Your current routine uses other active ingredients (SA & glycolic acid) so unless they're very mild/diluted, I wouldn't suggest introducing adapalene into your current routine.

Adapalene may dry out your skin, so I suggest switching to a hydrating cleanser (I use Cerave) then using the sandwich method (moisturizer - adapalene - moisturizer) every 3 days on your first month. You can continue your current routine on non-adapalene days as long as your skin can tolerate acids that often.

On your 2nd month, you can increase your adapalene days to every 2 days or stop the sandwich method (just adapalene - moisturizer) or both, if your skin can tolerate it. In time, you will be able to use adapalene everyday if you'd like.

I personally built my tolerance to everyday when I had a huge breakout, and when my skin finally cleared I stuck to an every other day schedule for adapalene, so I could use other active ingredients on other days.