
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, each circle is divided into unequal areas by a horizontal line, and $O$ is the center of the larger circle. The area of the larger circle is $100\pi.$ The line divides the larger circle such that the shaded lower semi-circle is $\frac{2}{3}$ of its total area. The smaller circle’s center is located 2 units above $O$ and just touches the boundary of the larger circle. What is the total area of the shaded regions? [asy]
size(120);
import graph;
fill(Arc((0,0),2,180,360)--cycle,mediumgray);fill(Arc((0,2),1,0,180)--cycle,mediumgray);
draw(Circle((0,0),2));
draw(Circle((0,2),1));

dot((0,0)); label("$O$",(0,0),N);
draw((-2,0)--(2,0)); draw((-1,2)--(1,2));
[/asy]

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