
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
Four circles, each of radius 2, are externally tangent to each other and internally tangent to a larger circle. Find the radius of the large circle.

[asy]
draw(Circle((0,0),5),linewidth(0.7));
draw(Circle((-2,0),2),linewidth(0.7));
draw(Circle((2,0),2),linewidth(0.7));
draw(Circle((0,2*sqrt(3)),2),linewidth(0.7));
draw(Circle((0,-2*sqrt(3)),2),linewidth(0.7));
[/asy]

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