
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 that $a > b > 0$, the equation of the ellipse $C_{1}$ is $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$, and the equation of the hyperbola $C_{2}$ is $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$. The product of the eccentricities of $C_{1}$ and $C_{2}$ is $\frac{\sqrt{3}}{2}$. Determine the equations of the asymptotes of $C_{2}$.

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