
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 circles with centers $A$, $B$, and $C$, and radii $2$, $3$, and $4$, respectively, lying around line $m$, and Circle $A$ is externally tangent to Circle $B$, and Circle $B$ is internally tangent to Circle $C$, calculate the area of triangle $ABC$.

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