
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
If the radius of the incircle of a triangle is $r$, and the lengths of its three sides are $a$, $b$, and $c$, then the area $S$ of the triangle is given by $S = r(a + b + c)$. By analogous reasoning, if a tetrahedron has an inscribed sphere with radius $R$, and the areas of its four faces are $S_1$, $S_2$, $S_3$, and $S_4$, then the volume $V$ of the tetrahedron is equal to ______.

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