
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 \( y^2 = 4x \) is \( F \). Points \( A \) and \( B \) are on the parabola, and \( \angle AFB = \frac{2\pi}{3} \). The midpoint \( M \) of chord \( AB \) has a projection \( M' \) on the directrix \( l \). Find the maximum value of \( \frac{|MM'|}{|AB|} \).

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