
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
A circle with a radius of 2 is inscribed in triangle \(ABC\) and touches side \(BC\) at point \(D\). Another circle with a radius of 4 touches the extensions of sides \(AB\) and \(AC\), as well as side \(BC\) at point \(E\). Find the area of triangle \(ABC\) if the measure of angle \(\angle ACB\) is \(120^{\circ}\).

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