
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, centered at $A$, $B$, and $C$, have radii of $3$, $4$, and $5$, respectively, and are tangent to a common line $m$. Circle $B$ is at the center and its center is located at $(0, 4)$, tangent both to $m$ and externally to the other two circles. Circles $A$ and $C$ are on opposite sides of $B$, maintaining tangency. Calculate the area of triangle $ABC$.

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