
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, there are two circles. The larger circle has center $O$ and an area of $100\pi$. The smaller circle has its center on the circumference of the larger circle and touches the larger circle internally at one point. Each circle is divided into three equal areas, and we want to find the total area of the shaded regions which cover two of the three parts for each circle.
```asy
size(120);
import graph;
fill(Arc((0,0),2,240,480)--cycle,mediumgray);
fill(Arc((1,0),1,60,300)--cycle,mediumgray);
draw(Circle((0,0),2));
draw(Circle((1,0),1));
dot((0,0)); label("$O$", (0,0), W);
draw((-2,0)--(2,0));
draw((1,-1)--(1,1));
```

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