
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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