
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 with a side length of 12 cm has three quarter circles drawn with centers at three of the four corners. Calculate the area of the shaded region within the square that is not covered by the quarter circles. Express your answer in terms of $\pi$.

[asy]
unitsize (1.8 cm);
draw((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle);
filldraw(arc((1,1),1,270,180)--arc((-1,1),1,360,270)--arc((-1,-1),1,90,0)--cycle,gray);
[/asy]

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