
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 $C:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$ with an eccentricity of $4$, find the equations of its asymptotes.

A) $y = \pm \sqrt{15}x$
B) $y = \pm \frac{\sqrt{15}}{12}x$
C) $y = \pm \sqrt{3}x$
D) $y = \pm \frac{\sqrt{3}}{3}x$

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