
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 rests on a horizontal field. At a given time, the shadow of the sphere extends $20$ meters from the point where the sphere touches the ground. Simultaneously, a $1$-meter tall stick (held vertically with one end on the ground) casts a shadow of $4$ meters. Assuming the sun's rays are parallel, determine the radius of the sphere in meters.

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