
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 with a circumference of 50 feet travels at a speed of $r$ miles per hour. If the time for a complete rotation of the wheel is shortened by $\frac{1}{2}$ of a second, the speed $r$ increases by $10$ miles per hour. Find the original speed $r$.
A) 15
B) 18
C) 20
D) 22
E) 24

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