
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 the operation $\ast$ on sets $A$ and $B$ be defined as $A \ast B = \{ x \mid x = ab, a \in A, b \in B \}$. If $A = \{1, 2\}$ and $B = \{0, 2\}$, find the sum of all elements in $A \ast B$.

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