How to flatten plywood (or does it matter)?

I am making a 9" by 12" box. Top is hardwood raised panel, box is hardwood, base is hardwood ... but I was planning to use a piece of 1/4" plywood (walnut) for the bottom of the box.
This plywood bottom will be glued into grooves rabbitted into the inside top edge of the base. The box then glued on top of the base / plywood. The box's stock thickness is a hair under 1/2 " ... so about half of that sits on the plywood with the other half overlapping the base.
Here's my question: the plywood sheet from which I cut my bottom piece was a bit curled ... when I cut out the roughly 9*12 bottom piece it curled even moret. The edges now curl up about 1" when it's just lying on my workbench. I am ready to glue/clamp this plywood down on my base ... but now I'm worried that this curling will cause trouble for my box on down the road. Do you think the glue will hold up over time? Or will the constant pull of the curling eventually cause something to give?
Rather than just glueing it "as is" I'm wondering about "plywood bending" (never tried it, but keep hearing about it). I wonder if I could use the same steam techniques used to bend plywood to just flatten out this little piece? If so, wonder exactly how I should go about it? Just steam it for a while or will the piece still require soaking (even though I'm not bending it much).
Thanks, Adam
(sitting here scratching my head ... the whole POINT of using plywood in the first place is to avoid this kind of problem!)
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Cut your plywood to size. Now lay the piece on a flat table. How much weight does it take to bring it to flat?
I suspect the answer would be less than a pound. if the edges are constrained in the dado, it will hold the panel flat, not to worry.
--

Roger Shoaf

About the time I had mastered getting the toothpaste back in the tube, then
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If the edges of a 9 inch by 12 inch piece of plywood are curling up 1 INCH at the edges, you need to get another sheet of plywood.

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