
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
In an equilateral triangle $ABC$, all three vertices lie on the surface of a sphere with center $O$. $G$ is the centroid of the triangle $ABC$, and $OG = \frac{\sqrt{3}}{3}$. The area of the circumcircle of triangle $ABC$ is $\frac{2\pi}{3}$. Calculate the volume of the sphere.

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