
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 hyperbola that has the same foci as the ellipse $\frac{x^{2}}{40} + \frac{y^{2}}{15} = 1$ and an eccentricity of $e = \frac{5}{4}$.

(2) Given that the center of an ellipse is at the origin, it passes through the point $P(3,2)$, its foci are on the $x$-axis, and the length of its major axis is three times the length of its minor axis, find the equation of the ellipse.

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