
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 $n= \overset{ .}{abc}$ represent a three-digit number, and define $f(n) = (a+b+c) + (ab+bc+ac) + abc$. For example, $f(123) = (1+2+3) + (1 \times 2 + 1 \times 3 + 2 \times 3) + 1 \times 2 \times 3 = 23$. Find the total number of three-digit numbers that satisfy $f(n) = n$.

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