
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 truncated cone has horizontal bases with radii 12 and 4, and the height of the cone from the larger base to the smaller is 15 units. A sphere is tangent to the inside surfaces of the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere?

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