
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 cylindrical bucket with a bottom diameter of $32 \text{ cm}$ is partially filled with water. After placing a metal ball in the water, fully submerging it, the water level rises by $9 \text{ cm}$ (without overflowing). Calculate the surface area of the ball in $\text{cm}^2$.

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