
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
Suppose the inradius of a triangle is $r$, and the lengths of its three sides are $a$, $b$, and $c$. The area of the triangle is $S=\frac{1}{2}r(a+b+c)$. By analogy, if the inradius of a tetrahedron is $R$, and the areas of its four faces are $S\_1$, $S\_2$, $S\_3$, and $S\_4$, then the volume of this tetrahedron is $V=$ \_\_\_\_\_\_.

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