
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 large sphere is placed in a sunny field. At noon, the shadow cast by the sphere extends 12 meters from the point of contact with the ground. At the same time, a pole that is 3 meters tall casts a shadow of 4 meters. Assuming the sun's rays are parallel, find the radius of the sphere.

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