
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's call a non-empty (finite or infinite) set \( A \) consisting of natural numbers complete if, for any natural numbers \( a \) and \( b \) (not necessarily distinct and not necessarily belonging to \( A \)), such that \( a+b \) is in \( A \), the number \( ab \) is also in \( A \). Find all complete sets of natural numbers.

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