
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
Positive integers  $a_0<a_1<\dots<a_n$ , are to be chosen so that  $a_j-a_i$  is not a prime for any  $i,j$  with  $0 \le i <j \le n$ . For each  $n \ge 1$ , determine the smallest possible value of  $a_n$ .

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