
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In triangle $ABC$, $AC = 8$, $BC = 15$, and angle $C$ is a right angle. Point $M$ is the midpoint of $AB$, and point $D$ is such that $AD = BD = 17$ and is on the same side of $AB$ as $C$. Find the area of triangle $CDM$ and express it as $\frac{m\sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers, $m$ and $p$ are relatively prime, and $n$ is not divisible by the square of any prime.

Present the answer in LaTex format: \boxed{Your answer}
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