
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 \( n \geq 2 \) be an integer. Find the maximal cardinality of a set \( M \) of pairs \((j, k)\) of integers, \( 1 \leq j < k \leq n \), with the following property: If \((j, k) \in M\), then \((k, m) \notin M\) for any \( m \).

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