
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 points \\(A\\), \\(B\\), and \\(C\\) are on the surface of a sphere \\(O\\), with \\(AB=BC=CA=3\\), and the distance from the center \\(O\\) of the sphere to the plane \\(ABC\\) is equal to one-third of the radius of the sphere, then the surface area of the sphere \\(O\\) is \_\_\_\_\_\_.

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