
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
Inside a sphere, there is a fixed point \( P \). There are three moving points \( A \), \( B \), and \( C \) on the sphere’s surface such that \( \angle BPA = \angle CPA = \angle CPB = 90^\circ \). Using \( PA \), \( PB \), and \( PC \) as edges, construct a parallelepiped. Point \( Q \) is the vertex of the parallelepiped that is diagonally opposite to point \( P \). As \( A \), \( B \), and \( C \) move on the sphere’s surface, determine the locus of point \( Q \).

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