
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 an integer  $ n > 3$ . Denote the set  $ T\equal{}\{1,2, \ldots,n\}.$  A subset S of T is called *wanting set* if S has the property: There exists a positive integer  $ c$  which is not greater than  $ \frac {n}{2}$  such that  $ |s_1 \minus{} s_2|\ne c$  for every pairs of arbitrary elements  $ s_1,s_2\in S$ . How many does a *wanting set* have at most are there ?

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