
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
For each positive integer \( n \), let \( a_n \) be the smallest nonnegative integer such that there is only one positive integer at most \( n \) that is relatively prime to all of \( n, n+1, \ldots, n+a_n \). If \( n < 100 \), compute the largest possible value of \( n - a_n \).

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