
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
Three circles of radius 2 are externally tangent to each other and internally tangent to a larger circle. Determine the distance from the center of the large circle to the point of tangency on one of the small circles. Express your answer in terms of radical expressions where suitable.

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