
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
An angle of $120^{\circ}$ is inscribed in a circle with a radius of 12 such that the center of the circle lies on the angle's bisector. Find the area of the part of the circle that is outside the angle.

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