
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
Let \( n \) be a given positive integer. Find the smallest positive integer \( u_n \) such that, for every positive integer \( d \), the number of numbers divisible by \( d \) in any \( u_n \) consecutive positive odd numbers is no less than the number of numbers divisible by \( d \) in the set of odd numbers \( 1, 3, 5, \ldots, 2n-1 \).

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