
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 \( n \) (\( n \geq 5 \)) distinct real numbers \( a_{1} < a_{2} < \cdots < a_{n} \), the necessary and sufficient condition for exactly \( 2n - 3 \) distinct sums among \( \frac{1}{2} n(n-1) \) sums \( a_{i} + a_{j} \) (\( 1 \leq i, j \leq n, i \neq j \)) is that \( a_{1}, a_{2}, \cdots, a_{n} \) form an arithmetic sequence.

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