
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 the ellipse C₁: $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a＞b＞0) with one focus coinciding with the focus of the parabola C₂: y<sup>2</sup>\=4 $$\sqrt {2}$$x, and the eccentricity of the ellipse is e= $$\frac { \sqrt {6}}{3}$$.
(I) Find the equation of C₁.
(II) A moving line l passes through the point P(0, 2) and intersects the ellipse C₁ at points A and B. O is the origin. Find the maximum area of △OAB.

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