
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
Let $\triangle ABC$ be a right triangle with right angle at $C$. Let $I$ be the incenter of $\triangle ABC$, and let $M$ lie on $AC$ and $N$ on $BC$ such that $M$, $I$, and $N$ are collinear and $\overline{MN}$ is parallel to $\overline{AB}$. If $AB = 36$ and the perimeter of $\triangle CMN$ is 48, find the area of $\triangle ABC$.

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