
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 parabola $C:y^{2}=6x$ and its focus $F$, the line passing through $F$ intersects $C$ at points $A$ and $B$. Let $l_{1}$ and $l_{2}$ be the tangents to $C$ at points $A$ and $B$, respectively. If $l_{1}$ and $l_{2}$ intersect at point $P$ and $|PF|=2\sqrt{3}$, determine the distance $|AB|$.

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