
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
An ice ballerina rotates at a constant angular velocity at one particular point with her arms initially extended. Her moment of inertia is $I$. When she pulls her arms in, her new moment of inertia is $\frac{7}{10}I$. Calculate the ratio of the new kinetic energy (with arms in) to the initial kinetic energy (with arms out).

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