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To answer the two Qs separately: Yes, you can do this if you obtain written permission from AP for your 'for-profit' use of their published work. You are protected by copyright law for citations / copying passages of the AP work for purposes of "fair use". This is kind of a gray area meaning that you can quote parts of it for criticism and reference. "How much" and "what types of criticism are valid" are undefined. In general, it would be considered a violation of their copyright for you to cite or copy (without permission) their article extensively (and copying it onto the cover of your book would be "extensive") in a way that does not also serve them, or in a way that harms them.
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