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I don’t see a way for Black to stop the pawns after Qg7+
There might be something better, but doesn’t Qg7+ Q:g7, B:g7 force a new Q?
There might be better, but Qg7+ Q:g7, B:g7 forces a new Q.
d7-d8Q!
Qg7 check should be good enough.
d7-d8Q
Qg7+ QxQ
BxQ wins easily
Qg7 is the way.
If 1. d8, Rxd8; 2. Qxf4, Qxe7, white will be very hard pressed to win.
Qg7 looks like the cleanest, surest way to win without screwing it up, but d8Q also appears to win, but there are more lines you have to check to be sure.