
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
Find the standard equation of the ellipse that satisfies the following conditions:
1. The foci of the ellipse are on the X-axis, the length of the major axis is three times the length of the minor axis, and it passes through point $A(3,0)$.
2. The center of the ellipse is at the origin, with the coordinate axes as its axes of symmetry, and it passes through points $P_{1}(\sqrt{6},1)$ and $P_{2}(-\sqrt{3},-\sqrt{2})$.

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