
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
On line $\overline{AE}$, points $B$, $C$, and $D$ are positioned such that $\overline{AB}$ is 3 times the length of $\overline{BD}$, and $\overline{AD}$ is 5 times the length of $\overline{CD}$. If $E$ is a point on the extension of $\overline{AD}$ such that $\overline{DE} = \overline{AD}$, what fraction of the length of $\overline{AE}$ is $\overline{BC}$?
A) $\frac{1}{40}$
B) $\frac{1}{20}$
C) $\frac{1}{30}$
D) $\frac{1}{10}$
E) $\frac{1}{50}$

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