
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, symmetric axes aligned with the coordinate axes, one vertex at $A(0,2)$, and the distance between its right focus $F$ and point $B( \sqrt {2}, \sqrt {2})$ is $2$.
(I) Find the equation of the ellipse;
(II) Let line $l$ passing through point $(0,-3)$ intersect the ellipse at two distinct points $M$ and $N$ such that $| \overrightarrow{AM}|=| \overrightarrow{AN}|$, find the equation of line $l$.

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