
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
In a board, the positive integer  $N$  is written. In each round, Olive can realize any one of the following operations:
I - Switch the current number by a positive multiple of the current number.
II - Switch the current number by a number with the same digits of the current number, but the digits are written in another order(leading zeros are allowed). For instance, if the current number is  $2022$ , Olive can write any of the following numbers  $222,2202,2220$ .
Determine all the positive integers  $N$ , such that, Olive can write the number  $1$  after a finite quantity of rounds.

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