Alternatively: How do I take a non-square PNG and "fill out" the "rest" of the image with transparency so that the resulting square image has the original image centered in the square?

ULTIMATELY, what I want is to take any image of any GM-supported format of any size, and create a scaled-down PNG (say, 40 pixels maximum for either dimension), with aspect ratio maintained, transparency-padded for non-square original images, AND with an already-prepared 40x40 PNG transparency mask applied.

I already know how to scale down and keep aspect ratio; I already have the command for applying my composite. My only missing piece is square-alizing non-square images (padding with transparency).

Single command preferred; multi-command chain acceptable.

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Extra info: Here's the composite command I'm using:

gm composite -compose copyopacity mask.png source-and-target.png source-and-target.png

where mask.png has white pixels for what I want to keep of source-and-target.png and transparent pixels for what I want to remove (and become transparent) of source-and-target.png.