
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 $\triangle ABC$ be an isosceles triangle with $AB = AC = 2x$ and $BC = x$. Extend side $\overline{AB}$ beyond $B$ to a point $B'$ so that $BB' = 2 \cdot AB$. Extend side $\overline{AC}$ beyond $C$ to a point $C'$ so that $CC' = 2 \cdot AC$. What is the ratio of the area of $\triangle AB'C'$ to the area of $\triangle ABC$? Assume $x > 0$ for all calculations.
A) 3:1
B) 5:1
C) 7:1
D) 9:1
E) 11:1

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