
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
Let $DEF$ be an equilateral triangle. Extend side $\overline{DE}$ beyond $E$ to a point $E'$ so that $EE' = 2 \cdot DE$. Similarly, extend side $\overline{EF}$ beyond $F$ to a point $F'$ so that $FF' = 2 \cdot EF$ and extend side $\overline{FD}$ beyond $D$ to a point $D'$ so that $DD' = 2 \cdot FD$. Determine the ratio of the area of $\triangle D'E'F'$ to the area of $\triangle DEF$.
A) $3:1$
B) $6:1$
C) $9:1$
D) $12:1$
E) $15:1$

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