
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 with its center at the origin and its axes along the coordinate axes, one of its vertices is A(0, 2), and the distance from its right focus F to the point $B(\sqrt{2}, \sqrt{2})$ is 2.  
(I) Find the equation of the ellipse;  
(II) Suppose a line $l$ passing through the point (0, -3) intersects the ellipse at two distinct points M and N such that $|\overrightarrow{AM}| = |\overrightarrow{AN}|$, try to find the equation of line $l$.

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