
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 liquid of mass \( M \) fills a cylindrical glass up to a height \( H \). The glass is rotated around its axis with such an angular velocity that the liquid rises to a height of \( 2H \) at the edge of the glass (refer to the diagram).

a) What is the velocity of the liquid at the edge of the glass?

b) What is the kinetic energy of the liquid?

c) What is the minimum work required to accelerate the liquid?

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