
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 \( n \) and \( k \) be integers, with \( 1 < k \leq n \). Find an integer \( b \) and a set \( A \) of \( n \) integers satisfying the following conditions:

1. No product of \( k-1 \) distinct elements of \( A \) is divisible by \( b \).
2. Every product of \( k \) distinct elements of \( A \) is divisible by \( b \).
3. For all distinct \( a, a^{\prime} \) in \( A \), \( a \) does not divide \( a^{\prime} \).

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