
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
Starting with any three-digit number \( n \), we form a new number \( f(n) \), which is the sum of the three digits of \( n \), the products of the digits taken two at a time, and the product of the three digits.
1. When \( n = 625 \), compute \( \frac{n}{f(n)} \).
2. Find all three-digit numbers such that \( \frac{n}{f(n)} = 1 \).

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