
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
A parabola $y^2=8x$ and a hyperbola $C: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, (a > 0, b > 0)$ are given. The distance between one of the asymptotes of the hyperbola and the focus of the parabola is $\sqrt{3}$. Determine the eccentricity of the hyperbola $C$.

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