
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 $PQR$ be an equilateral triangle. Extend side $\overline{PQ}$ beyond $Q$ to a point $Q'$ so that $QQ'=2 \cdot PQ$. Similarly, extend side $\overline{QR}$ beyond $R$ to a point $R'$ so that $RR'=2 \cdot QR$, and extend side $\overline{RP}$ beyond $P$ to a point $P'$ so that $PP'=2 \cdot RP$. Determine the ratio of the area of $\triangle P'Q'R'$ to the area of $\triangle PQR$.
A) 4
B) 6
C) 7
D) 9
E) 16

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