
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
Point A is the intersection point of one of the asymptotes of the hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > 0,b > 0)$ and the parabola $y^{2}=2px(p > 0)$. If the distance from point A to the directrix of the parabola $C1$ is $p$, then calculate the eccentricity of the hyperbola $C2$.

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