
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
Consider a central circle with radius 2. Three smaller circles of radius \( r \) are tangent to each other and tangent to the larger circle. The centers of the smaller circles are collinear. What is the radius \( r \) of the smaller circles?

[asy]
unitsize(0.6 cm);
draw(Circle((0,0),4),linewidth(0.7));
draw((0,0)--(4,0));
label("2",(2,0),S);
for(int i=0; i<3; ++i){
  draw(Circle((6+i*4,0),2),linewidth(0.7)); 
  draw((4+2*i,0)--(6+2*i,0));
  label("$r$",(5+2*i,0),S);
}
[/asy]

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