
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 an ellipse that satisfies the following conditions:
(1) The coordinates of the two foci are (-2, 0) and (2, 0), and the sum of the distances from a point P on the ellipse to the two foci is equal to 6. Find the equation of the ellipse.
(2) The foci of the ellipse are F1(0, -5) and F2(0, 5), and point P(3, 4) is on the ellipse. Find the equation of the ellipse.

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