
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
Consider a rectangle where one pair of opposite vertices are the centers of two circles. Each side of the rectangle adjacent to these centers is 10 cm, and the radius of each circle is 3 cm. The other pair of sides of the rectangle are 12 cm. Find the area in square centimeters of the shaded region, where the shading represents the intersection of the rectangle with only the area inside both circles.
[asy]
fill( (0,0)-- (12,0) -- (12,10) -- (0,10)--cycle, gray);
fill( Circle((0,0), 3), white);
fill( Circle((12,10), 3), white);
draw( Arc((0,0),3 ,90,270));
draw( Arc((12,10),3,270,450));
draw( (0,0)-- (12,0) -- (12,10) -- (0,10)--cycle,linewidth(.8));
[/asy]

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