
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]


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Given the hyperbola ${x}^{2}-\frac{{y}^{2}}{3}=1$, let $F_{1}$ be the left focus of the hyperbola. A line passing through $F_{1}$ at an angle of $\frac{π}{6}$ intersects the hyperbola at points $A$ and $B$. Find the length of $|AB|$.

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