
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
Find all positive integer  $n$  , such that for all 35-element-subsets of  $M=(1,2,3,...,50)$  ,there exists at least two different elements  $a,b$  , satisfing :  $a-b=n$  or  $a+b=n$ .

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