
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
In the polar coordinate system, given the line l: p(cosθ + sinθ) = 2 and the curve C: C: p = 4cosθ.
(1) If the line l intersects the curve C at two points A and B, find the distance |AB|.
(2) If point P is any point on the curve other than A and B, find the maximum area of △PAB.

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