
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 $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{9} = 1$ and passes through the point $(4,3)$.

(2) Find the standard equation of the hyperbola that has the same asymptotes as the hyperbola $\dfrac{x^{2}}{4} - \dfrac{y^{2}}{9} = 1$ and has a focal length of $2\sqrt{13}$.

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