
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, all natural numbers from 1 to 100 inclusive are written. Vasya picks a pair of numbers from the board, whose greatest common divisor is greater than one, and erases one of them. What is the smallest number of numbers that Vasya can leave on the board after performing such actions?

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