
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
Find all the positive integers  $N$  with an even number of digits with the property that if we multiply the two  numbers formed by cutting the number in the middle we get a number that is a divisor of  $N$  ( for example  $12$  works because  $1 \cdot 2$  divides  $12$ )

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