
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
Let \( n \) be a five-digit number (the first digit is not zero), and \( m \) be the four-digit number formed by removing the middle digit of \( n \). Determine all \( n \) such that \( \frac{n}{m} \) is an integer.
(Canadian Mathematical Olympiad, 1971)

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