
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 parabola $y^2 = 8x$ has its focus at point $F$ and its directrix as the line $l$. Let $P$ be a point on the parabola and let $PA$ be perpendicular to $l$ with $A$ being the foot of the perpendicular. If the slope of the line $AF$ is $- \sqrt {3}$, then find the length of $|PF|$.

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