
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
The center of the ellipse is at the coordinate origin, and the ratio between the lengths of the major and minor axes is $2:1$. One focus point is $(0, -2)$. Find the eccentricity and the standard equation of the ellipse.

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