
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 $C:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ with its right vertex at point $A$, a circle $A$ is created with center at $A$ and radius $b$. Circle $A$ intersects with one of the asymptotes of hyperbola $C$ at points $M$ and $N$. If $\angle MAN = 60^{\circ}$, find the eccentricity of hyperbola $C$.

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