
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 configuration below, the largest circle has a radius of 10 meters. Three identical smaller circles are placed inside and are touching each other as shown, forming a straight line from one point on the circumference of the larger circle to another point directly opposite. What is the radius in meters of one of the three smaller circles?

[asy]
size(3cm,3cm);
draw(Circle((0,0),1));
draw(Circle((-2,0),1));
draw(Circle((2,0),1));
draw(Circle((0,0),3));
[/asy]

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