
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
Define an operation between sets A and B: $A*B = \{x | x = x_1 + x_2, \text{ where } x_1 \in A, x_2 \in B\}$. If $A = \{1, 2, 3\}$ and $B = \{1, 2\}$, then the sum of all elements in $A*B$ is ____.

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