
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  $n\geq 2$  be an integer. Determine all sets of real numbers  $(a_1, a_2,\dots, a_n)$  such that  $a_1-2a_2, a_2-2a_3,\dots, a_{n-1}-2a_n, a_n-2a_1$  are rearrangements of  $a_1, a_2,\dots, a_n$ . 

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