
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
The focus of the parabola \( y^{2}=2px \) \( (p>0) \) is point \( F \), and the directrix is line \( l \). Points \( A \) and \( B \) are on the parabola and satisfy \( \angle AFB=\frac{\pi}{3} \). Let \( M \) be the midpoint of segment \( AB \), and let \( N \) be the projection of \( M \) onto \( l \). Find the maximum value of \( \frac{|MN|}{|AB|} \).

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