
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 \(P\). On the surface of the sphere, there are three moving points \(A\), \(B\), and \(C\). Given that \(\angle BPA = \angle CPA = \angle CPB = 90^\circ\), a parallelepiped is formed using \(PA\), \(PB\), and \(PC\) as its edges. Point \(Q\) is the vertex of this parallelepiped that is diagonally opposite to \(P\). Find the locus of point \(Q\) as \(A\), \(B\), and \(C\) move on the surface of the sphere.

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