
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 a circle with equation $x^2 + y^2 = 16$ and center P, suppose there is a point Q(a, b) outside of circle P. A circle M is drawn with diameter PQ and intersects circle P at points A and B.  
(1) Determine the position relationship between the lines QA, QB, and circle P. If QA = QB = 3, find the equation of the curve on which point Q lies.  
(2) If a = 4 and b = 6, find the equation of the line AB.

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