
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  $A$  be the set  $A = \{ 1,2, \ldots, n\}$ . Determine the maximum number of elements of a subset  $B\subset A$  such that for all elements  $x,y$  from  $B$ ,  $x+y$  cannot be divisible by  $x-y$ . 

*Mircea Lascu, Dorel Mihet*

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