
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 the parabola $C: y^2 = 4x$ with focus point $F$ and directrix $l$, a line passing through point $F$ intersects the parabola $C$ at points $A$ and $B$. A perpendicular line to the directrix $l$ is drawn through point $A$, and the foot of the perpendicular is $E$. If the angle $\angle AFE = 75^\circ$, find the length of $|AE|$.

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