
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
Definition of Set Operation: $A*B=\\left\\{ \\left. z \\right|z=xy,x\\in A,y\\in B \\right\\}.$ Given $A=\\left\\{ 1,2 \\right\\}$ and $B=\\left\\{ 0,2 \\right\\}$, find the sum of all elements in the set $A*B$.

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