
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 $C$: $y^{2}=2px (p > 0)$ with focus $F$, and the directrix line $l$ intersecting the $x$-axis at point $A$. Point $P$ lies on parabola $C$ such that $PF \perp x$-axis. If the chord length intercepted by the circle with diameter $AF$ on the line segment $AP$ is $2$, find the value of the real number $p$.

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