
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 a new configuration, a large circle has a radius of 10 meters. Six smaller circles of equal size are arranged such that each smaller circle touches the larger circle internally at exactly one point, forming a regular hexagonal pattern inside. If the centers of the smaller circles form a regular hexagon, what is the radius of one of the smaller circles?

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