
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
For any three-digit number \( n \), let \( \overline{n} \) represent the number obtained by removing all digits equal to 0 from \( n \). For example, if \( n = 102 \), then \( \overline{n} = 12 \). How many three-digit numbers \( n \) satisfy \( \overline{n} < n \) and \( \overline{n} \) is a divisor of \( n \)?

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