
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
A large square has each side divided into four equal parts. A square is inscribed such that its vertices touch these division points, as illustrated below. Determine the ratio of the area of the inscribed square to the large square.
[asy]
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle);
draw((1,0)--(1,0.1)); draw((2,0)--(2,0.1)); draw((3,0)--(3,0.1));
draw((4,1)--(3.9,1)); draw((4,2)--(3.9,2)); draw((4,3)--(3.9,3));
draw((1,4)--(1,3.9)); draw((2,4)--(2,3.9)); draw((3,4)--(3,3.9));
draw((0,1)--(0.1,1)); draw((0,2)--(0.1,2)); draw((0,3)--(0.1,3));
draw((1,0)--(4,3)--(3,4)--(0,1)--cycle);
[/asy]
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) $\frac{5}{8}$
D) $\frac{3}{4}$

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