What does Snow tell Katniss in the rose room? What does this ultimately lead Katniss to do?

Snow, who is dying, tells Katniss that Coin ordered both the parachutes and the massacre. He told her that he had no purpose in killing all of those children, and although Katniss doesn't believe him, he causes her to doubt what she knows. In respnse to what she learns, Katniss shoots and kills Coin with her bow.