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I’m going to be installing LVP glue down due to my floors being not flat enough for a floating install. They look like this for the most part.

Is it fine to screw down 3/8″ – 1/2″ plywood to my subfloor? Am I correct in thinking screwing it down will result in a better connection with the old subfloor?

Do I need to use a floor leveling compound on this plywood bit? It’s a 1/4″ shy of the surface at it’s worst. Or would skim coat be enough with plywood going overtop of it?