Repair water-damaged top

[asousa]

Hello, I just purchased an old Jacobean buffet for a steal at $10! It does have some damage but all in all its in decent shape. The top however is damaged. The veneer was lifted as was the thin layer of wood underneath. My plan was to remove the damaged veneer, fill the uneven space, sand and paint it dark in color. As I removed the top layer I noticed the very bottom layer was water damaged and dark spots. This layer is strips of wood that almost look like furring strips. How could i repair this area? Replace the strip? I've never had to do this type of repair on a piece so I'm new to this!