
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 from any three-digit number \( n \), we obtain a new number \( f(n) \) by summing the three digits of \( n \), the sum of the products of each pair of digits, and the product of the three digits.
(1) When \( n=625 \), find the integer value of \( \frac{n}{f(n)} \).
(2) Find all 3-digit numbers \( n \) such that \( \frac{n}{f(n)}=1 \).

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