
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
Triangle $ABC$ is a right triangle with $AC = 8$, $BC = 15$, and right angle at $C$. Point $M$ is the midpoint of $AB$, and $D$ is on the same side of line $AB$ as $C$ so that $AD = BD = 17$. Given that the area of triangle $CDM$ may be expressed 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, find $m + n + p$.

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