
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
Consider an equilateral triangle $ABC$. Extend side $\overline{AB}$ by twice its length to reach a new point $D$, the extension on side $\overline{BC}$ is three times its own length to a point $E$, and on side $\overline{CA}$ by four times to a point $F$. Determine the ratio of the area of triangle $DEF$ to that of triangle $ABC$.

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