
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 points A(1, 0) and B(-1, 0), the equation of circle C is x^2 + y^2 - 6x - 8y + 16 = 0. Point P is a moving point on the circle, and the length of the chord intercepted by line l passing through point A on circle C is $2\sqrt{5}$.

(1) Find the equation of line l.
(2) Find the maximum area of triangle PAB.

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