Where did black go wrong??

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This is a game played by a computer where white outplayed his opponent tactically. What moves could black have made to improve its play?

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The actual mate sequence that took place was:

28... Kh7 29. Qd7+ Qg7 30. Qf5+ Qg6 31. Rf7+ Kg8 32. Qxg6+ Kh8
33. Qg7#