
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 curve that fits the following conditions.

(1) An ellipse with a minor axis of 6 and an eccentricity of $e=\frac{2\sqrt{2}}{3}$.

(2) A hyperbola that shares the same foci as the ellipse $4x^{2}+9y^{2}=36$ and passes through the point $(4,\sqrt{3})$.

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