
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 square is inscribed in a circle. Another smaller square has one side coinciding with one side of the larger square and has two vertices on the circle. Assume the side length of the larger square is 4 units. Determine what percent of the area of the larger square is occupied by the area of the smaller square.

[asy]
draw(Circle((0,0),2*sqrt(2)));
draw((2,2)--(2,-2)--(-2,-2)--(-2,2)--cycle);
draw((0.4,2)--(0.4,2.8)--(-0.2,2.8)--(-0.2,2));
[/asy]

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