
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 the plane, if a convex polygon has an inscribed circle, then the relationship between the area ($S$), the perimeter ($c$), and the radius of the inscribed circle ($r$) is $S=\frac{1}{2}cr$. By analogy, in space, if a convex polyhedron has an inscribed sphere with radius ($R$), what is the relationship between the volume ($V$), the surface area ($S'$), and the sphere radius ($R$)?

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