
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 A*B be the set defined by $A*B=\{z|z=xy, x \in A, y \in B\}$, where $A=\{1, 2\}$ and $B=\{0, 1, 2\}$. Find the sum of the elements of all subsets of the set $A*B$.

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