
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 the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 (a>0, b>0)$ is $2$, and the focus of the parabola $y^{2}=4x$ is $F$, a line $l$ passing through $F$ intersects the parabola at points $A$ and $B$. If the line $l$ is parallel to one of the asymptotes of the hyperbola, then find the length of segment $AB$.

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