
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 lying in $A$), for which $a + b$ lies in $A$, the number $ab$ also lies in $A$. Find all complete sets of natural numbers.

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