
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
There are  $\tfrac{n(n+1)}{2}$  distinct sums of two distinct numbers, if there are  $n$  numbers.
For which  $n \ (n \geq 3)$  do there exist  $n$  distinct integers, such that those sums are  $\tfrac{n(n-1)}{2}$  consecutive numbers?

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