
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 hemisphere is placed on a sphere of radius \(100 \text{ cm}\). The second hemisphere is placed on the first one, and the third hemisphere is placed on the second one (as shown below). Find the maximum height of the tower (in cm).

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