
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 set of pairs of natural numbers $(i, j)$ where $1 \leq i < j \leq n$ for a fixed $n \geq 2$. If a pair $(i, j)$ belongs to $M$, then no pair $(j, k)$ can belong 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}
user