
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  $n\ge 3$ . consider a sequence  $a_1,a_2,...,a_n$ , if  $(a_i,a_j,a_k)$  with i+k=2j (i<j<k) and  $a_i+a_k\ne 2a_j$ , we call such a triple a  $NOT-AP$  triple. If a sequence has at least one  $NOT-AP$  triple, find the least possible number of the  $NOT-AP$  triple it contains.

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