
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 three points A, B, and C on the surface of a sphere, the distance from the plane determined by these points to the center of the sphere is equal to half of the sphere's radius, and AB = BC = CA = 2. Determine the surface area of the sphere.

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