
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 \(ABC\) be an equilateral triangle. Extend side \( \overline{AB} \) beyond \( B \) to a point \( B' \) so that \( BB' = 4 \cdot AB \). Similarly, extend side \( \overline{BC} \) beyond \( C \) to a point \( C' \) such that \( CC' = 4 \cdot BC \), and extend side \( \overline{CA} \) beyond \( A \) to a point \( A' \) so that \( AA' = 4 \cdot CA \). Calculate the ratio of the area of \( \triangle A'B'C' \) to the area of \( \triangle ABC \).
A) \( 36 \)
B) \( 16 \)
C) \( 25 \)
D) \( 49 \)

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