I would use 3/4 T X G Advantec with constrution adhesive on the joist, instead of plywood. There's little squares printed right on the panels to show where it needs to be nailed.
Advantec if far more stable, stiffer, and way more moisture resistant then plywood.
Make sure whatever plywood you use as an underlayment is subfloor rated.
That underlayment is going to have to be nailed every 4" on the edges, and every 6 to 8" in the field., it needs to not line up with the seams below, and not be nailed into the floor joist.
Advantec if far more stable, stiffer, and way more moisture resistant then plywood.
Make sure whatever plywood you use as an underlayment is subfloor rated.
That underlayment is going to have to be nailed every 4" on the edges, and every 6 to 8" in the field., it needs to not line up with the seams below, and not be nailed into the floor joist.