
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 $y^2 = 4x$, let $F$ be its focus. A line intersects the parabola at points $A$ and $B$. Let $l$ be the directrix of the parabola. The perpendiculars from $A$ and $B$ to $l$ meet $l$ at points $C$ and $D$ respectively. If $|AF| = 4|BF|$, find $|CD|$.

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