
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
An economist and a statistician play a game on a calculator which does only one
operation. The calculator displays only positive integers and it is used in the following
way: Denote by  $n$  an integer that is shown on the calculator. A person types an integer, $m$ , chosen from the set  $\{ 1, 2, . . . , 99 \}$  of the first  $99$  positive integers, and if  $m\%$  of the
number  $n$  is again a positive integer, then the calculator displays  $m\%$  of  $n$ . Otherwise,
the calculator shows an error message and this operation is not allowed. The game consists of doing alternatively these operations and the player that cannot do the operation
looses. How many numbers from  $\{1, 2, . . . , 2019\}$  guarantee the winning strategy for the
statistician, who plays second?

For example, if the calculator displays  $1200$ , the economist can type  $50$ , giving the number $600$  on the calculator, then the statistician can type  $25$  giving the number  $150$ . Now, for
instance, the economist cannot type  $75$  as  $75\%$  of  $150$  is not a positive integer, but can
choose  $40$  and the game continues until one of them cannot type an allowed number

*Proposed by Serbia*

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