
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 circle C: (x+2)²+y²=9 and point P(0,1), a line passes through point P and intersects the circle at points A and B.
(1) If the chord length |AB|=4√2, find the slope of line AB.
(2) Find the maximum area of ∆ABC and the chord length |AB| in this case.

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