
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 a parabola $C$: $y^{2}=2px (p > 0)$ with its focus $F$, a line $l$ passing through $F$ with a slope angle of $60^{\circ}$ intersects the parabola $C$ at points $A$ and $B$ in the first and fourth quadrants, respectively, and intersects its axis at point $P$. Find the value of $\frac{|AB|}{|AP|}$.

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