
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 major and minor axes of an ellipse are aligned with the coordinate axes, one endpoint of the minor axis and the two foci form an equilateral triangle, and the shortest distance from a focus to a point on the ellipse is $\sqrt{3}$. Determine the equation of the ellipse.

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