
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
Square $IJKL$ is inscribed within square $WXYZ$ such that each vertex of $IJKL$ touches one side of $WXYZ$. If point $I$ is on side $WZ$ with $WI = 9 \cdot IZ$, find the ratio of the area of square $IJKL$ to the area of square $WXYZ$.
A) $\frac{1}{32}$
B) $\frac{1}{50}$
C) $\frac{1}{64}$
D) $\frac{1}{100}$
E) $\frac{1}{128}$

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