
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 $R$, points $A$, $B$, and $C$ are on the surface of sphere $O$. The distance from the center of the sphere $O$ to the plane $ABC$ is $\frac{1}{2}R$. It is given that $AB=AC=2$ and $\angle BAC=120^{\circ}$. Find the surface area of sphere $O$.

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