In triangle $ABC$, $\angle C$ is a right angle. Point $M$ is the midpoint of the hypotenuse $AB$. Given that $AC = 8$ units, $BC = 6$ units, and point $D$ is on the hypotenuse $AB$ such that $AD = 5$ units and $BD = 5$ units. Find the length of the median $CM$ and the area of triangle $CMD$. Let's think step by step and output the final answer within \boxed{}.
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