
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
Let two natural number  $n > 1$  and  $m$  be given. Find the least positive integer  $k$  which has the following property: Among  $k$  arbitrary integers  $a_1, a_2, \ldots, a_k$  satisfying the condition  $a_i - a_j$  (  $1 \leq i < j \leq k$ ) is not divided by  $n$ , there exist two numbers  $a_p, a_s$  ( $p \neq s$ ) such that   $m + a_p - a_s$  is divided by  $n$ .

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