
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
Find the kinetic energy of a circular cylinder with height \( h \) and density varying according to the law \( \rho(r) = \rho_{0} + k r \), where \( 0 \leq r \leq R \), \( r \) is the distance from the axis of the cylinder, \( R \) is the radius of the base, if the cylinder rotates around its axis with a constant angular velocity \( \omega \).

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