
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 the diagram, two concentric circles are drawn with $O$ as their common center. The outer circle is divided into two equal areas, and the inner circle has two-thirds of its area shaded. If the area of the larger circle is $81\pi,$ determine the total area of the shaded regions. The diagram is as follows: 
[asy]
size(100);
import graph;
fill(Arc((0,0),2,180,360)--cycle,mediumgray);fill(Arc((0,0),1,0,240)--cycle,mediumgray);
draw(Circle((0,0),2));
draw(Circle((0,0),1));

dot((0,0)); label("$O$",(0,0),N);
draw((-2,0)--(2,0)); draw((-1,0)--(cos(240*pi/180),sin(240*pi/180))); //indicates 240 degrees, approximately.
[/asy]

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