
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 a positive integer  $n$ , let  $S(n), P(n)$  denote the sum and the product of all the digits of  $n$  respectively.
1) Find all values of n such that  $n = P(n)$ :
2) Determine all values of n such that  $n = S(n) + P(n)$ .

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