
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
Let $S-ABC$ be a triangular prism with circumscribed sphere centered at $O$. The midpoints of $SB$ and $AC$ are $N$ and $M$, respectively. The midpoint of line segment $MN$ is $P$, and it is given that $SA^{2} + SB^{2} + SC^{2} = AB^{2} + BC^{2} + AC^{2}$. If $SP = 3\sqrt{7}$ and $OP = \sqrt{21}$, find the radius of sphere $O$.

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