
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 ball is floating in a water-filled prism-shaped glass. If the ball is removed, by how much does the water level drop in the glass, given that the bottom of the glass is a regular hexagon with each side measuring $5 \mathrm{~cm}$, the radius of the floating ball is $4 \mathrm{~cm}$, and the section of the ball protruding from the water is $1 \mathrm{~cm}$ high?

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