
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 of radius 18 rolls along a circle of radius 40. A nail is driven into the wheel, and as the nail hits the circumference of the circle, it leaves marks on it. How many such marks will the nail leave on the circle? How many times will the wheel roll along the entire circumference before the nail hits a previously marked point?

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