
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 \( M \) be a subset of the set of all pairs of natural numbers \( i < k \), not exceeding a given natural number \( n \geqslant 2 \). Furthermore, if the pair \( i < k \) belongs to the set \( M \), then no pair \( k < m \) belongs to it. What is the maximum number of pairs that can be in the set \( M \)?

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