
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, the area of a triangle is $S$, and its perimeter is $C$. The radius of the incircle is $\gamma= \frac {2S}{C}$. In space, the volume of a triangular pyramid is $V$, and the surface area is $S$. By using analogical reasoning, the radius $R$ of the insphere (the sphere tangent to each face of the triangular pyramid) is \_\_\_\_\_\_.

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