
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 inscribed circle of a triangle is $r$, and the lengths of its three sides are $a$, $b$, and $c$, then the area of the triangle is $S=\frac{1}{2}r(a+b+c)$; by analogy, if the radius of the inscribed sphere 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 the tetrahedron is .

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