
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 $C: y^2 = 16x$ with the focus $F$, and the line $l: x = -1$, if a point $A$ lies on $l$ and the line segment $AF$ intersects the parabola $C$ at point $B$ such that $\overrightarrow{FA} = 5\overrightarrow{FB}$, then find the length of $|AB|$.

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