
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 $y^{2}=8x$ with focus $F$ and directrix $l$. Let $P$ be a point on the parabola such that $PA \perp l$, where $A$ is the foot of the perpendicular. If the slope of the line $AF$ is $-1$, find the value of $|PF|$.

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