
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
David, Kevin, and Michael each choose an integer from the set  $\{1, 2, \ldots, 100\}$  randomly, uniformly, and independently of each other. The probability that the positive difference between David's and Kevin's numbers is  $\emph{strictly}$  less than that of Kevin's and Michael's numbers is  $\frac mn$ , for coprime positive integers  $m$  and  $n$ . Find  $100m + n$ .

*Proposed by Richard Yi*

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