
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 the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) with its right focus at point $F$, and point $A$ is on the asymptote of the hyperbola. If $\triangle OAF$ is an equilateral triangle with side length $6$ ($O$ is the origin), then the equation of the hyperbola is \_\_\_\_\_\_.

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