
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
Consider a parabola given by the equation $y^{2}=2px$ with $p > 0$. Let $F$ be the focus of the parabola, and let two perpendicular rays emanate from $F$, intersecting the parabola at points $M$ and $N$. Draw a line through the midpoint $P$ of the chord $MN$ that is perpendicular to the parabola's axis, and let $Q$ be the foot of this perpendicular line. What is the maximum value of $\frac{|PQ|}{|MN|}$?

A) $\frac{\sqrt{2}}{2}$

B) $\frac{1}{2}$

C) $1$

D) $\frac{\sqrt{3}}{3}$

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