
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
On a board the numbers  $(n-1, n, n+1)$  are written where   $n$  is positive integer. On a move choose 2 numbers  $a$  and  $b$ , delete them and write  $2a-b$  and  $2b-a$ . After a succession of moves, on the board there are 2 zeros. Find all possible values for  $n$ .
Proposed by Andrei Eckstein

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