
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
Given the natural number \( n \geq 2 \). Let \( M \) be a subset of the set \( \{(i, k) \mid i, k \in \mathbb{N}, i < k \leq n \} \). It is known that if the pair \( (i, k) \), where \( i < k \), belongs to the set \( M \), then any pair \( (k, m) \), where \( k < m \), does not belong to \( M \). Find the maximum number of elements in the set \( M \).

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