
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 foci of the hyperbola $C$, a line passes through $F\_1$ and is perpendicular to the real axis of the hyperbola, intersecting the hyperbola at points $A$ and $B$. If $\triangle F\_2AB$ is an equilateral triangle, find the eccentricity of the hyperbola, denoted as $e=$ \_\_\_\_\_\_\_\_.

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