
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
Assuming the point on the short axis of an ellipse and its two foci form an equilateral triangle, and the shortest distance from a focus to the endpoint of the ellipse's major axis is $\sqrt {3}$, determine the equation of the ellipse with its foci on the y-axis.

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