
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 \( 0 = a_0 < a_1 < \cdots < a_n = 2n - 1 \). Find 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}
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