
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 plane rectangular coordinate system xOy, an ellipse with the equation $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}$$\=1 (a＞b＞0) has an eccentricity of $$\frac { \sqrt {6}}{3}$$, and its major axis is of length 2 $$\sqrt {3}$$. The line l: y=kx+2 intersects the ellipse at two distinct points A and B.
(I) Find the equation of the ellipse.
(II) When the area of △AOB equals $$\frac {6}{7}$$, find the equation of line l.

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