
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
Given the hyperbola $C$ with the equation $9y^{2} - 16x^{2} = 144$.

(1) Find the lengths of the transverse and conjugate axes, the coordinates of the foci, and the eccentricity of the hyperbola $C$.

(2) Find the equation of the hyperbola that has the same asymptotes as hyperbola $C$ and passes through point $P(6, 4)$.

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