
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 center \( O_1 \) and radius 2 is inscribed in triangle \( ABC \) and touches side \( BC \) at point \( D \). A second circle with center \( O_2 \) and radius 4 touches the extensions of sides \( AB \) and \( AC \), as well as side \( BC \) at point \( E \). Find the area of quadrilateral \( O_1 D O_2 E \), given that the measure of angle \( ACB \) is \( 120^\circ \).



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