
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 $B$, $C$, and $E$ lie on $\overline{AD}$. The length of $\overline{AB}$ is $3$ times the length of $\overline{BD}$, and the length of $\overline{AC}$ is $5$ times the length of $\overline{CD}$. Point $E$ is such that the length of $\overline{DE}$ is $2$ times the length of $\overline{EA}$. The length of $\overline{BC}$ is what fraction of the length of $\overline{AD}$?
A) $\frac{1}{12}$
B) $\frac{1}{10}$
C) $\frac{1}{8}$
D) $\frac{1}{6}$
E) $\frac{1}{4}$

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