
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 given point \( P \). Points \( A, B, \) and \( C \) are located on the surface of the sphere such that \( PA, PB, \) and \( PC \) are mutually perpendicular to each other. Let \( Q \) be the vertex of the rectangular cuboid defined by \( PA, PB, \) and \( PC \) that is opposite to \( P \). What is the locus of the points \( Q \)?

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