
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 parabola $C\_1:y^{2}=8x$ with focus $F$, and $P$ is a point on the parabola $C\_1$ located in the first quadrant, with $|PF|=4$. The distance from $P$ to one asymptote of the hyperbola $C\_2: {x^{2} \over a^{2}}- {y^{2} \over b^{2}}=1 (a > 0, b > 0)$ is $2$. Find the eccentricity of the hyperbola $C\_2$.

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