
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, 5, and 4 respectively. These circles are tangent to a line m at points A', B', and C' respectively, with B' between A' and C'. The circle centered at B is externally tangent to the other two circles. Calculate the area of triangle ABC.

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