
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
When a lake is frozen, a ball is floating on its surface. After removing the ball (without breaking the ice), a hole with a top diameter of $24 \mathrm{~cm}$ and a depth of $8 \mathrm{~cm}$ is left on the ice. Calculate the radius of the ball.

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