
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 asymptotes of the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1 \ (a > 0, b > 0)$ are the lines containing sides $OA$ and $OB$ of the equilateral triangle $OAB$ (where $O$ is the origin). If the line $AB$ passes through the focus of the hyperbola and $|AB| = 2$, then $a = $ ______.

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