
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
Given a uniform circular disk of radius  $R$  and mass  $M$ , the moment of inertia about an axis through the center of the disk and perpendicular to the plane of the disk is  $I_\text{0}=\frac{1}{2}MR^2$ ; a hole is cut in the disk. Determine the moment of inertia of the resulting object about the axis shown in terms of  $R$  and  $M$ .

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