
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 equations of the ellipse under the following conditions:  
(1) It shares a common focus with the ellipse $\frac {x^{2}}{9}+ \frac {y^{2}}{4}=1$ and passes through point M(3, -2);  
(2) Its center is at the origin, its foci are on the coordinate axes, and it passes through points $A( \sqrt {3}, -2)$ and $B(-2 \sqrt {3}, 1)$.

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