
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 top of a sphere with a radius of 2017. A second hemisphere is then placed on top of the first hemisphere, and a third hemisphere is placed on top of the second hemisphere. All the centers are collinear, and the three hemispheres have empty interiors and negligible width. What is the maximum height of this tower made up of the sphere and three hemispheres?

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