
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
(1) Find the standard equation of the ellipse that has the same foci as the ellipse $9x^{2}+4y^{2}=36$ and passes through the point $(-2,3)$.

(2) Find the standard equation of the hyperbola that has the same asymptotes as the hyperbola $\dfrac{x^{2}}{2}-y^{2}=1$ and passes through the point $(2,-2)$.

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