
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 positive integer \( n \geqslant 5 \), find:
(1) The minimum number of distinct sums \( a_{i} + a_{j} \) (\(1 \leqslant i < j \leqslant n\)) in a set of \( n \) elements \(\left\{a_{1}, a_{2}, \cdots, a_{n}\right\}\);
(2) Identify all such sets of \( n \) elements that achieve the minimum value found in part (1).

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