
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 \( P \) be a fixed point inside a sphere. From point \( P \), three mutually perpendicular rays intersect the surface of the sphere at points \( A \), \( B \), and \( C \) respectively. Point \( Q \) is the vertex of the rectangular parallelepiped formed by \( PA \), \( PB \), and \( PC \) that is diagonally opposite to point \( P \). Determine the locus of points \( Q \) corresponding to all possible sets of three rays drawn from point \( P \).

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