
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
A circle of radius 2 is surrounded by 4 circles of radius \(r\) as shown in a similar diagram. Determine the radius \(r\) necessary for the arrangement.

[asy]
unitsize(0.6cm);
for(int i=0; i<2; ++i){
for(int j=0; j<2; ++j){
draw(Circle((-3.2+6.4i,-3.2+6.4j),3.2),linewidth(0.7));
draw((-3.2+6.4i,-3.2+6.4j)--(-0.95+6.4i,-0.95+6.4j));
label("$r$",(-2.1+6.4i,-2.1+6.4j),SE);
};
}
draw(Circle((0,0),2),linewidth(0.7));
draw((0,0)--(2,0));
label("2",(1,0),S);
[/asy]

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