
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\\)_: \\(\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1\\) (_\\(a > 0\\)_, _\\(b > 0\\)_) with its right vertex at _\\(A\\)_, a circle with center _\\(A\\)_ and radius _\\(b\\)_ is drawn, intersecting one of the asymptotes of the hyperbola _\\(C\\)_ at points _\\(M\\)_ and _\\(N\\)_. If \\(∠MAN = 60^\circ\\), then the eccentricity of _\\(C\\)_ is _______.

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