
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 diagram, there are three smaller circles positioned inside a larger circle. Each smaller circle touches the other two smaller circles exactly at the center of the larger circle. The radius of the larger circle is 9. Calculate the area of the shaded region outside the smaller circles but inside the larger circle.

[asy]
size(100);
import graph;
filldraw(Circle((0,0),3),mediumgray);
filldraw(Circle((-1.5,0),1.5),white);
filldraw(Circle((1.5,0),1.5),white);
filldraw(Circle((0,1.5*sqrt(3)),1.5),white);
[/asy]

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