
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
Maxim came up with a new method for dividing numbers by a two-digit number \( N \). To divide an arbitrary number \( A \) by the number \( N \), you need to do the following steps:
1) Divide \( A \) by the sum of the digits of \( N \);
2) Divide \( A \) by the product of the digits of \( N \);
3) Subtract the second result from the first.

For which numbers \( N \) will Maxim’s method give the correct result? (20 points)

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