
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 \( S_n \) be the set of all strictly decreasing sequences of \( n \) positive integers such that no term divides any other term. Given two sequences \( A = (a_i) \) and \( B = (b_j) \), we say that \( A < B \) if for some \( k \), \( a_k < b_k \) and \( a_i = b_i \) for \( i < k \). For example, \( (7, 5, 3) < (9, 7, 2) < (9, 8, 7) \). Find the sequence \( A \) in \( S_n \) such that \( A < B \) for any other \( B \) in \( S_n \).

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