
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 $C_{1}$: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1 \ (a > 0, b > 0)$ passes through the focus of the parabola $C_{2}$: $y^{2} = 2px \ (p > 0)$, and the asymptotes of the hyperbola form an equilateral triangle with the directrix of the parabola, calculate the eccentricity of the hyperbola $C_{1}$.

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