
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 $ABC$, it's a right triangle with $AC = 9,$ $BC = 40,$ and the right angle at $C$. Point $M$ is the midpoint of $AB,$ and $D$ is located on the same side of line $AB$ as $C$ such that $AD = BD = 26.$ Find the area of triangle $CDM$, which can be expressed in the form $\frac{x\sqrt{y}}{z}$ where $x, y, z$ are positive integers, $x$ and $z$ are relatively prime, and $y$ is not divisible by the square of any prime.

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