
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 with centers at \(A\), \(B\), and \(C\), have radii \(2\), \(3\), and \(4\) respectively. They lie to the left of line \(m\) and are tangent to it at points \(A'\), \(B'\), and \(C'\), respectively. The order of tangency points from left to right on line \(m\) is \(B'\), \(A'\), \(C'\). The circle at \(B\) is externally tangent to the two other circles. Determine the area of triangle \(ABC\).

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