
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 given circle with a radius of 3, six equal circles are inscribed, each tangent to the given circle and also to two neighboring circles. Find the radii of the inscribed circles.

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