
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 \( k \) and \( n \) be integers such that \( 1 \leq k \leq n \). What is the maximum number of \( k \)-element subsets of the set \(\{1, 2, \ldots, n\}\) such that for any two of these subsets, one is composed of the \( k \) smallest elements of their union?

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