
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 \( A, B, \) and \( C \) have radii \( 3, 4, \) and \( 5 \), respectively. They are on the same side of line \( m \) and are tangent to \( m \) at points \( A', B', \) and \( C' \), respectively, with \( B' \) between \( A' \) and \( C' \). The circle at \( B \) is externally tangent to the other two circles. Calculate the area of triangle \( ABC \).
A) \( 4 \)
B) \( 6 \)
C) \( 8 \)
D) \( 10 \)

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