
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
For a positive integer  $n$ , there is a school with  $2n$  people. For a set  $X$  of students in this school, if any two students in  $X$  know each other, we call  $X$  *well-formed*. If the maximum number of students in a well-formed set is no more than  $n$ , find the maximum number of well-formed set. 

Here, an empty set and a set with one student is regarded as well-formed as well.

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