
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 that the center of ellipse $E$ is at the origin $O$, its foci lie on the $x$-axis, and the square formed by the endpoints of the minor axis and the foci of ellipse $E$ has a sum of distances from any point on the ellipse to the two foci equal to $2\sqrt{2}$.

(I) Find the standard equation of ellipse $E$.

(II) If line $l$: $y=2x+m$ intersects ellipse $E$ at points $M$ and $N$, find the maximum area of $\triangle MON$.

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