
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 an equilateral triangle $ABC$ with side length $a$ and area $s$, the radius of the inscribed circle is $r=\frac{2s}{3a}$. By analogy, for a regular tetrahedron $S-ABC$ with the base area $S$, the radius of the inscribed sphere is $R$, and the volume is $V$, then $R=$_______.

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