
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 with radius $R$, there are three points on the surface of the sphere. The spherical distance between any two points is $\frac {\pi R}{3}$. If the circumference of the small circle passing through these three points is $4\pi$, then $R=\boxed{2\sqrt{3}}$.

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