
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
For which natural numbers \( n \geq 3 \) is it possible to obtain a set of \( n \) identical numbers from the set of numbers \( 1, 2, \ldots, n \) in a finite number of steps, if at each step, we can choose any two numbers and increase each of them by an arbitrary identical natural number?

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