
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
In rectangle $ABCD$, $DC = 3 \cdot CB$ and points $E$ and $F$ lie on $\overline{AB}$ so that $\overline{ED}$ and $\overline{FD}$ trisect $\angle ADC$ as shown. What is the ratio of the area of $\triangle DEF$ to the area of rectangle $ABCD$?
- $\textbf{A)}\ \frac{\sqrt{3}}{36}$
- $\textbf{B)}\ \frac{\sqrt{3}}{18}$
- $\textbf{C)}\ \frac{\sqrt{3}}{12}$
- $\textbf{D)}\ \frac{\sqrt{3}}{24}$
- $\textbf{E)}\ \frac{\sqrt{3}}{48}$

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