
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 isosceles triangle where $AB = AC$ and $\overline{BC}$ is the base. Extend side $\overline{AB}$ beyond $B$ to a point $B'$ such that $BB' = 2 \cdot AB$. Similarly, extend side $\overline{AC}$ beyond $C$ to a point $C'$ such that $CC' = 2 \cdot AC$. Also, extend side $\overline{BC}$ from both points $B$ and $C$ to points $B''$ and $C''$ such that $BB'' = BC'' = 2 \cdot BC$. Determine the area ratio of $\triangle B''BC''$ to $\triangle ABC$.
A) 16:1
B) 25:1
C) 36:1
D) 49:1
E) 64:1

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