
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
There are  $n \ge 2$  numbers on the blackboard:  $1, 2,..., n$ . It is permitted to erase two of those numbers  $x,y$  and write  $2x - y$  instead. Find all values of  $n$  such that it is possible to leave number  $0$  on the blackboard after  $n - 1$  such procedures.

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