
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
The code of a combination lock is a two-digit number. Buratino forgot the code, but he remembers that the sum of the digits of this number, added to their product, equals the number itself. Write down all possible code options so that Buratino can quickly open the lock.

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