
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
For a given integer  $n\ge 2$ , let  $a_0,a_1,\ldots ,a_n$  be integers satisfying  $0=a_0<a_1<\ldots <a_n=2n-1$ . Find the smallest possible number of elements in the set  $\{ a_i+a_j \mid 0\le i \le j \le n \}$ .

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