
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 an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ (a > b > 0) and a hyperbola $\frac{x^{2}}{m^{2}} - \frac{y^{2}}{n^{2}} = 1$ (m > 0, n > 0) that share common foci, and b = n. Where the eccentricity of the ellipse is $\frac{\sqrt{3}}{2}$, find the equations of the asymptotes of the hyperbola.

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