
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
Diagrams $X$, $Y$, and $Z$ consist of two equilateral triangles and a square, respectively. Equilateral triangle $X$ has an area of $75\sqrt{3}$ square inches, and equilateral triangle $Y$ has an area of $48\sqrt{3}$ square inches. Square $Z$ has a side length of $12$ inches. If the length of segment $ZR$ is decreased by $12\tfrac{1}{2}$% of itself, while the lengths of segments connecting the triangles to the square remain unchanged, calculate the percent decrease in the area of square $Z$.
A) 12.5%
B) 25%
C) 50%
D) 75%
E) 87.5%

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