
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 the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{3} = 1$, find the equation of the ellipse that has the foci of the hyperbola as its vertices and the vertices of the hyperbola as its foci.

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