
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 each side of the triangle beyond each vertex so that $BB' = 2 \cdot AB$, $CC' = 2 \cdot BC$, and $AA' = 2 \cdot CA$. Determine the ratio of the area of triangle $A'B'C'$ to the area of $\triangle ABC$.

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