
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  $ n$  be a nonzero positive integer. Find  $ n$  such that there exists a permutation  $ \sigma \in S_{n}$  such that
\[ \left| \{ |\sigma(k) \minus{} k| \ : \ k \in \overline{1, n} \}\right | = n.\]

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