
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 $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a＞0，b＞0)$, $A_1$, $A_2$ are the left and right vertices of the hyperbola, respectively. $M(x_0, y_0)$ is a point on the hyperbola other than the two vertices. The product of the slopes of lines $MA_1$ and $MA_2$ is $\frac {16}{9}$. Find the eccentricity of the hyperbola. If the distance from the focus of the hyperbola to its asymptote is 4, find the equation of the hyperbola.

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