
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
Two circles of radius 12 have their centers on each other. \( A \) is the center of the left circle, and \( AB \) is a diameter of the right circle. A smaller circle is constructed tangent to \( AB \) and the two given circles, internally to the right circle and externally to the left circle. Find the radius of the smaller circle.

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