
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
Given that point \( P(3,4) \) is inside the circle \( x^2 + y^2 = 64 \). There are two moving points \( A \) and \( B \) on the circumference of the circle such that \( \angle APB = \frac{\pi}{2} \). A rectangle \( APBQ \) is formed with \( AP \) and \( BP \) as adjacent sides. Find the equation of the trajectory of point \( Q \).

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