
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
Write the standard equation of the ellipse that meets the following conditions:  
(1) $a=6$, $c=3\sqrt{3}$, and the foci are on the x-axis;  
(2) The coordinates of the two foci are $F_1(0, -2)$, $F_2(0, 2)$, and it passes through point $A(3, 2)$.

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