How to remove cultured marble bathroom vanity countertop?

I will be replacing my existing cultured marble bathroom vanity countertop with a new cultured marble countertop. I am not replacing the vanity; it is brand new. So first I need to remove the existing countertop without damaging any of the vanity wood. The countertop is not screwed into the vanity. Instead there is a bead of adhesive between the countertop and the vanity, and there is a silicone caulk bead between the edge of the vanity and the tile on the wall.

I assume I can use a utility knife to cut the silicone caulk at the edge of the vanity.

But how do I loosen the adhesive between the vanity so that I can lift off the old countertop, and do this without damaging the vanity wood? What tools and techniques do I use?

Always tricky,
Cut what you can from the caulking, they pry from inside the box with a flat Stanley Wonder Bar.

You might not get it off without damage. Many of the cabinets are made with a veneer over particle board - the better ones over plywood.