
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 numbers on the blackboard, then erase one of them and replace it with the sum of the other two minus 1. After repeating this process several times, the numbers on the board become $(17, 1967, 1983)$. Determine if the original three numbers on the blackboard could have been (1) $(2, 2, 2)$; (2) $(3, 3, 3)$.

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