
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 is inscribed in a sector that is one-sixth of a circle of radius 6. (That is, the circle is tangent to both segments and the arc forming the sector.) Find, with proof, the radius of the small circle.

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