
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 spherical decoration was suspended in a cylindrical container when the water inside it froze. The decoration was removed (without breaking the ice), leaving a hole 30 cm across at the top and 10 cm deep. If the water froze up to a height of 5 cm from the top of the sphere, what was the radius of the sphere (in centimeters)?

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