
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 a set $A=\{a_1, a_2, a_3, \ldots, a_n\}$, denote the number of distinct values in the sums $a_i + a_j$ ($1 \leq i < j \leq n$) as $M(A)$. For example, when $A=\{1, 2, 3, 4\}$, since $1+2=3$, $1+3=4$, $1+4=2+3=5$, $2+4=6$, $3+4=7$, we have $M(A)=5$. If $A=\{1, 2, 3, \ldots, n\}$, then $M(A)=$    .

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