
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  $S_n$  be the set of all permutations of  $(1,2,\ldots,n)$ . Then find :
\[ \max_{\sigma \in S_n} \left(\sum_{i=1}^{n} \sigma(i)\sigma(i+1)\right) \]
where  $\sigma(n+1)=\sigma(1)$ .

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