
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, $n$ non-negative integers are written. The GCD of these $n$ integers is 1. An operation consists of replacing two integers $x$ and $y$ (if $x \leq y$) with $2x$ and $y-x$. For which initial configurations is it possible, after a certain number of operations, to end with $n-1$ zeros written on the board?

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