
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
Given right triangle $\triangle ABC$ has a hypotenuse $AC$ of length 10, where $A$ is at the right angle. Point $M$ is the midpoint of hypotenuse $\overline{AC}$, and $D$ is a point on leg $\overline{AB}$ such that $AD:DB = 1:2$. Determine the area of $\triangle ADM$.

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