
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
100 pairwise distinct natural numbers \( a_{1}, a_{2}, \ldots, a_{100} \) are written on a board. Then, under each number \( a_{i} \), the number \( b_{i} \) is written, obtained by adding to \( a_{i} \) the greatest common divisor of the remaining 99 original numbers. What is the smallest possible number of pairwise distinct numbers among \( b_{1}, b_{2}, \ldots, b_{100} \)?

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