
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
Janine is creating a design using a large square and inside it are placed six small circles. Each circle is tangent to one side of the square and the three circles adjacent to it. The side length of the square in Janine's design is 30 inches. How many square inches will be shaded in her design?

[asy]
size(120);
draw((0,0)--(6,0)--(6,6)--(0,6)--cycle);

fill((0,0)--(6,0)--(6,6)--(0,6)--cycle,grey);

draw(circle((1,1),1)); 
fill(circle((1,1),1),white);
draw(circle((5,1),1)); 
fill(circle((5,1),1),white);
draw(circle((1,5),1)); 
fill(circle((1,5),1),white);
draw(circle((5,5),1)); 
fill(circle((5,5),1),white);

draw(circle((3,2),1)); 
fill(circle((3,2),1),white);
draw(circle((3,4),1)); 
fill(circle((3,4),1),white);
[/asy]

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