
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 an eccentricity of $2$, derive the equation of its asymptotes.

A) $y = \pm 3x$
B) $y = \pm \frac{\sqrt{3}}{2}x$
C) $y = \pm \sqrt{3}x$
D) $y = \pm \frac{3}{2}x$

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