
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
After persistent searching, Andrey found a two-digit number which does not end in 0 and has a property such that, when inserting a 0 between its tens and units digits, it becomes a three-digit number divisible by the original two-digit number without a remainder. When he showed his result to the teacher, the teacher praised the boy and noted that not only the number Andrey found has this property. Find all such two-digit numbers. How many are there?

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