
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. Circle A and B are tangent to each other and on the same side of line m. Circle C is also on the same side of line m but not tangent to Circle A or B. Instead, Circle C is such that its center C is 1 unit away from line m. If Circle A is tangent to line m, find the area of triangle ABC.

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