
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 $F$ is the right focus of the hyperbola $C$: $x^2-\frac{y^2}{b^2}=1(a>0, b>0)$, a perpendicular line is drawn from point $F$ to the $x$-axis, intersecting the hyperbola and its asymptotes in the first quadrant at points $A$ and $B$ respectively. If $|AB|=|AF|$, then the equation of the asymptotes of the hyperbola $C$ is ______.

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