
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 $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$, where $A\_1$ and $A\_2$ are the left and right vertices, and $M(x\_0, y\_0)$ is a point on the hyperbola other than the two vertices. The product of the slopes of the lines $MA\_1$ and $MA\_2$ is $\frac{144}{25}$.
(1) Find the eccentricity of the hyperbola.
(2) If the distance from the focus of the hyperbola to the asymptote is 12, find the equation of the hyperbola.

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