
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
Write three integers on a blackboard, then erase one of them and replace it with the difference between the sum of the other two numbers and 1. Repeat this process several times until you get $(17, 1999, 2105)$. Can the three numbers initially written on the blackboard be $(2, 2, 2)$ or $(3, 3, 3)$?

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