
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
In a 6 by 6 grid, each of the 36 small squares measures 1 cm by 1 cm, and all are initially shaded. Six unshaded circles of different sizes are then placed on the grid as illustrated. The area of the visible shaded region can be written in the form $A-B\pi$ square cm. What is the value of $A+B$?

[asy]
for(int i = 0; i < 6; ++i)
{
    for(int j = 0; j < 6; ++j)
    {
        filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--cycle,gray,linewidth(2));
    }
}
filldraw(circle((1.5,1.5),0.5),white,linewidth(2));
filldraw(circle((4.5,1.5),0.5),white,linewidth(2));
filldraw(circle((1.5,4.5),0.5),white,linewidth(2));
filldraw(circle((4.5,4.5),0.5),white,linewidth(2));
filldraw(circle((3,3),1),white,linewidth(2));
filldraw(circle((3,3),0.5),white,linewidth(2));
[/asy]

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