
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
A circle has radius \( r \) and an internal point \( P \). A right angle with vertex \( P \) intersects the circle at points \( A \) and \( B \). The triangle \( BPA \) is completed to a rectangle \( PAQB \). What path does point \( Q \) trace as the right angle rotates around \( P \)?

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