
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
If  $1<k_1<k_2<...<k_n$  and  $a_1,a_2,...,a_n$  are integers such that for every integer  $N,$   $k_i \mid N-a_i$  for some  $1 \leq i \leq n,$  find the smallest possible value of  $n.$ 

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