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They are walking and suddenly it becomes such a simple thing to drop the gun and hold her tight in his arms. She is alive. He holds her, nuzzles her neck, squeezes her tight.
He is astonished that the Dalek didn't kill her or him. He is astonished that her simple, sweet touch infused that monster with humanity. It's astonishment that causes him to lay aside Time Lord rules, the reasons why he shouldn't and couldn't. He embraces Rose as if his life depended on it.
Of course his life depends on it. That part shouldn't astonish him at all.