
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 of $2, 3,$ and $4$ respectively. They all lie on the same side of line $m$ and are tangent to $m$ at points $A', B',$ and $C'$ respectively, with $B'$ located between $A'$ and $C'$. The circle with center $B$ is externally tangent to both of the other two circles. Find the area of triangle $ABC$.

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