
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 sphere is situated in an open field under sunlight. The shadow of the sphere casts a shadow reaching a distance of $12$ m from the point where the sphere touches the ground. Simultaneously, a $1.5$ m tall vertical pole casts a shadow of $3$ m. What is the diameter of the sphere, assuming that the rays of the sun are parallel and the sphere and pole are perfectly vertical?

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