Consider all quadrilaterals $ABCD$ such that $AB=14$, $BC=9$, $CD=7$, and $DA=12$. Find the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral. The original answer is in the form $k\sqrt{m}$, please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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