
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 the wheel with a circumference of $11$ feet, the speed $r$ in miles per hour for which the time for a complete rotation of the wheel is shortened by $\frac{1}{4}$ of a second is increased by $5$ miles per hour, find the value of $r$.

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