
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) with its left focus point F1(-1, 0), and point M(1, $$\frac { \sqrt {2}}{2}$$) is on the ellipse. A line l passes through the origin O and intersects the ellipse C at points A and B. Point P is on the ellipse C (and is not coincident with A or B).
(1) Find the equation of the ellipse C;
(2) If the slope of line AB is -$$\frac {1}{2}$$, find the maximum area of △ABP.

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