
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 $\triangle ABC$ with side lengths $a$, $b$, and $c$, and the area of $\triangle ABC$ is $S$, and the radius of the inscribed circle is $r$, then $r=$; By analogy, for a tetrahedron $S-ABC$ with the areas of its four faces being $S_1$, $S_2$, $S_3$, and $S_4$, and the radius of the inscribed sphere being $R$, and the volume of the tetrahedron $P-ABC$ being $V$, then $R=$ ( )

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