
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 an ellipse with its center at the origin and passing through point $P(3,2)$, with its foci on the coordinate axes, and the length of its major axis is three times the length of its minor axis, find the equation of the ellipse.

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