
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

From the numbers \(1, 2, \cdots, n+1\), remove one number, and arrange the remaining numbers into a sequence \(a_{1}, a_{2}, a_{3}, \cdots, a_{n}\) such that the \(n\) differences \(\left|a_{1}-a_{2}\right|, \left|a_{2}-a_{3}\right|, \cdots, \left|a_{n}-a_{1}\right|\) are all different. For which values of \(n\) (where \(n \geq 3\)) can this requirement be satisfied?

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