
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
Given circles with centers $A$, $B$, and $C$ have radii $2$, $3$, and $4$ respectively. They all lie on the same side of the inclined line $m$ making an angle of $30^\circ$ with the horizontal, and are tangent to $m$ at $A'$, $B'$, and $C'$, respectively, with $B'$ between $A'$ and $C'$. The circle with center $B$ is externally tangent to each of the other two circles. Calculate the area of triangle $ABC$.

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