
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 $2$, $3$, and $4$ respectively. They are all tangent to the same line $m$ at points $A'$, $B'$, and $C'$, where $B'$ is between $A'$ and $C'$. The circle at $B$ is externally tangent to the other two circles. Calculate the area of triangle $ABC$.
- **A**: $5$
- **B**: $6$
- **C**: $7$
- **D**: $8$

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