
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 $F\_1$ and $F\_2$ are the two foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} =1 (a > 0, b > 0)$, and if $F\_1$, $F\_2$, and $P(0, 2b)$ are the three vertices of a right triangle, find the equations of the asymptotes of the hyperbola.

A) $y=± \frac{\sqrt{21}}{7} x$
B) $y=± \frac{\sqrt{21}}{3} x$
C) $y=± \frac{\sqrt{3}}{3} x$
D) $y=± \sqrt{3} x$

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