
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
Points $A$, $B$, $C$, $D$, and $E$ are located on a line segment $\overline{AB}$ such that $AB = 4AD = 8BE = 2BC$. What is the probability that a point randomly chosen on $\overline{AB}$ lies between $B$ and $E$? 

[asy]
draw((0,0)--(16,0.000000001));
dot((0,0)); dot((4,0)); dot((8,0)); dot((12,0)); dot((16,0));
label("$A$", (0,0), S);
label("$D$", (4,0), S);
label("$E$", (8,0), S);
label("$B$", (12,0), S);
label("$C$", (16,0), S);
[/asy]

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