
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 following curves.

(1) An ellipse that passes through the point $(-3,2)$ and has the same foci as $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$.

(2) A hyperbola that passes through the point $(2,-1)$ with asymptotes $y = \pm 3x$.

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