
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 $B$ and $C$ are on line segment $\overline{AD}$. It is known that the length of $\overline{AB}$ is 3 times the length of $\overline{BD}$, and the length of $\overline{AC}$ is 8 times the length of $\overline{CD}$. What is the length of $\overline{BC}$ as a fraction of the length of $\overline{AD}$?
A) $\frac {1}{36}$
B) $\frac {1}{13}$
C) $\frac {1}{10}$
D) $\frac {5}{36}$
E) $\frac {1}{5}$

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