
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
Let  $F$  be the focus of parabola  $y^2=2px(p>0)$ , with directrix  $l$  and two points  $A,B$  on it. Knowing that  $\angle AFB=\frac{\pi}{3}$ , find the maximal value of  $\frac{|MN|}{|AB|}$ , where  $M$  is the midpoint of  $AB$  and  $N$  is the projection of  $M$  to  $l$ .

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