
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 $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) with asymptotes that intersect the circle $x^2 + y^2 - 6x + 5 = 0$ to form a chord of length 2, find the eccentricity of the hyperbola. The options are:
A) $\frac{\sqrt{6}}{2}$
B) $\frac{3}{2}$
C) $\sqrt{6}$
D) 2

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