
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
The right focus of the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ is $F$, and its left and right vertices are $A_{1}$ and $A_{2}$, respectively. A perpendicular line to $A_{1}A_{2}$ passing through $F$ intersects the hyperbola at points $B$ and $C$. If $A_{1}B \perp A_{2}C$, then the slope of the asymptotes of this hyperbola is ______.

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