
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
Given a triangle $ABC$ with side lengths $a$, $b$, $c$ and area $S$, and an inscribed circle $O$ with radius $r$. Connect $OA$, $OB$, $OC$. Then, the areas of triangles $OAB$, $OBC$, $OAC$ are respectively $\frac{1}{2}cr$, $\frac{1}{2}ar$, $\frac{1}{2}br$. From $S= \frac{1}{2}cr+ \frac{1}{2}ar+ \frac{1}{2}br$, we get $r= \frac{2S}{a+b+c}$. By analogy, for a tetrahedron with volume $V$ and the areas of its four faces being $S_{1}$, $S_{2}$, $S_{3}$, $S_{4}$, the radius of the inscribed sphere $R=$ ______.

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