
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 $\overline{AD}$. 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 $\overline{CD}$. If the length of $\overline{AD}$ is 40 units, what fraction of $\overline{AC}$ is the length of $\overline{BD}$?
A) $\frac{1}{4}$
B) $\frac{1}{7}$
C) $\frac{2}{7}$
D) $\frac{1}{2}$
E) $\frac{1}{3}$

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