
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 an integer \( n \geqslant 2 \), let integers \( a_{0}, a_{1}, \cdots, a_{n} \) satisfy
\[ 0=a_{0}<a_{1}<\cdots<a_{n}=2n-1. \]

Determine the minimum possible number of elements in the set \( \left\{a_{i} + a_{j} \mid 0 \leqslant i \leqslant j \leqslant n \right\} \).

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