
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 homogeneous plate is bounded by two concentric ellipses with coinciding axes (an elliptical ring). Find the moments of inertia of this plate with respect to its axes.

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