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

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