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Step by step, you will make fast progress

I have a new approach: Qc2, threatening Qc7+ and Qc8++. If Rc3, then Qh2 and then Qh8++ (because now the rook covers the bishop). If, instead, Bc3, Qe4 and checkmate with Qa8. Can it be that way?

Excellent! Correct in every detail

Yes! It was difficult, but it finally came out!