
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
Wei has updated the design of his company's logo to include more circles within the same square frame. Each circle is still tangent to two sides of the square and to its adjacent circles. If the square's side length remains 20 inches, how many square inches will be shaded now?

[asy]
size(100);
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle);
fill((0,0)--(4,0)--(4,4)--(0,4)--cycle,grey);
draw(circle((1,1),2/3)); draw(circle((2,1),2/3)); draw(circle((3,1),2/3));
draw(circle((1,2),2/3)); draw(circle((2,2),2/3)); draw(circle((3,2),2/3));
draw(circle((1,3),2/3)); draw(circle((2,3),2/3)); draw(circle((3,3),2/3));
fill(circle((1,1),2/3),white); fill(circle((2,1),2/3),white); fill(circle((3,1),2/3),white);
fill(circle((1,2),2/3),white); fill(circle((2,2),2/3),white); fill(circle((3,2),2/3),white);
fill(circle((1,3),2/3),white); fill(circle((2,3),2/3),white); fill(circle((3,3),2/3),white);
[/asy]

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