
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 
$$\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$$
where \( a > 0 \) and \( b > 0 \), A<sub>1</sub> and A<sub>2</sub> are the left and right vertices of the hyperbola, respectively, and M(\( x_{0} \), \( y_{0} \)) is a point on the hyperbola other than the vertices. The product of the slopes of the lines MA<sub>1</sub> and MA<sub>2</sub> 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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