
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 an ellipse C: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0), O is the coordinate origin, F(-$$\sqrt {2}$$, 0) is the left focus of ellipse C, and the eccentricity is $$\frac { \sqrt {2}}{2}$$. The line l intersects the ellipse at points A and B.
(1) Find the equation of ellipse C;
(2) If M(1, 1) is the midpoint of chord AB, and P is a point on ellipse C, find the maximum area of △PAB.

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