
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 $C$ lie on line segment $\overline{AD}$. The length of $\overline{AB}$ is $3$ times the length of $\overline{BD}$, and the length of $\overline{AC}$ is $7$ times the length of $\overline{CD}$. Determine the fraction of the length of $\overline{AD}$ that is the length of $\overline{BC}$.

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