
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  $\{1,2,\ldots,n\}$ ,  $n\geq 2$ . Find the least number  $n$  for which there exist permutations  $\alpha$ ,  $\beta$ ,  $\gamma$ ,  $\delta$  of the set  $A$  with the property: \[ \sum_{i=1}^n \alpha(i) \beta (i) = \dfrac {19}{10} \sum^n_{i=1} \gamma(i)\delta(i) . \]
*Marcel Chirita*

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