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

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