
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
Consider a convex quadrilateral $ABCD$, where sides $AB,~ BC, ~CD$, and $DA$ are extended past $B,~ C ,~ D$, and $A$ to points $B',~C',~ D'$, and $A'$, respectively. Let $AB = BB' = 8$, $BC = CC' = 9$, $CD = DD' = 10$, and $DA = AA' = 11$. Each of the triangle areas outside $ABCD$ adjacent to each side are twice that of their corresponding side's triangle area within $ABCD$, yet $ABCD$ itself has an area of $15$. Calculate the total area of quadrilateral $A'B'C'D'$.
A) 30  
B) 40  
C) 45  
D) 50

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