
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 a sphere O with radius R, and three points A, B, C on the surface of sphere O. The distance from the center O to the plane ABC is $\frac{1}{2}R$. If AB=AC=2 and $\angle BAC=120^\circ$, then the surface area of sphere O is \_\_\_\_\_.

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