
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
Three circles of radii $2$, $3$, and $4$ are mutually externally tangent. Determine the area of the triangle formed by the points of tangency.
A) $6\sqrt{6}$
B) $6$
C) $9\sqrt{6}$
D) $18\sqrt{6}$
E) $12$

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