
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 \(B'\) such that \(BB' = 2 \cdot AB\). Extend side \(\overline{BC}\) beyond \(C\) to a point \(C'\) such that \(CC' = 4 \cdot BC\), and extend \(\overline{CA}\) beyond \(A\) to a point \(A'\) such that \(AA' = 3 \cdot CA\). 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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