
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) It is known that the center of an ellipse is at the origin, its foci lie on the x-axis, and its major axis is three times the length of its minor axis. The ellipse also passes through point P(3, 2). Find the equation of this ellipse.
(2) Find the equation of the hyperbola with a common asymptote with the hyperbola $\frac{x^2}{5} - \frac{y^2}{3} = 1$ and a focal length of 8.

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