
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
If the axes of symmetry of an ellipse are the coordinate axes, one endpoint of the minor axis and the two foci form an equilateral triangle, and the foci are on the $y$-axis with $a-c=\sqrt{3}$, what is the equation of the ellipse?

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