
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 foci of ellipse $E$ are on the $x$-axis, the center is at the origin, and the four vertices of a square with side length $2$ are on the minor axis and coincide with the foci, find the standard equation of ellipse $E$.

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