
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
Yura and Yasha are playing the following game, taking turns alternately. Yura goes first.

Initially, the number $n$ is written on the board. A player on their turn can add any natural divisor of the number on the board to it, erase the old number, and write down the new one. (For example, if the number 12 is written on the board, it can be erased and replaced with one of the numbers $13, 14, 15, 16, 18, 24$).

Consider all possible natural values of $n$ from 2 to 59 inclusive.

(a) For how many of them does Yura have a winning strategy if the player who receives a number not less than 60 after their move loses?

(b) For how many of them does Yura have a winning strategy if the player who receives a number not less than 60 after their move wins?

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