
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 $a > b > c$, 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 $\frac{2 \sqrt{2}}{3}$. Find the equations of the asymptotes of $C\_2$.

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