
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 wheel completes a full rotation, covering the distance from \(A\) to \(B\). The segment \(AB\) is equal to the circumference of the wheel. For instance, if the wheel has a diameter of 28 cm, its circumference can be calculated as approximately 88 cm. Now consider that the inner circle (hub) also makes a full rotation along the imaginary dashed line \(CD\), which is the same distance as \(AB\). Thus, the length of the smaller inner circle's path should be equal to \(AB\). Clearly, this seems incorrect. Where is the error? 

Try to identify the mistake. The hub rotates fully from \(C\) to \(D\), yet why is \(CD\) not equal to the circumference of the inner circle?

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