
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]


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In the tetrahedron \( S-ABC \),
\[ SA = SB = SC = \sqrt{21}, \quad BC = 6. \]

If point \( A \)'s projection onto the plane of face \( SBC \) is the orthocenter of triangle \( SBC \), find the volume of the inscribed sphere of tetrahedron \( S-ABC \).

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