
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
It is known that there are three boxes, _A_, _B_, and _C_, each containing two identical balls. In each box, one ball is labeled with the number 1, and the other ball is labeled with the number 2. Now, one ball is drawn from each of the _A_, _B_, and _C_ boxes.  
(1) If the numbers on the balls drawn from the _A_, _B_, and _C_ boxes are represented by _x_, _y_, and _z_ in the array (_x_, _y_, _z_), please list all possible scenarios for the array (_x_, _y_, _z_) and answer how many different scenarios there are in total;  
(2) If you were asked to guess the sum of the numbers on these three balls, with a prize for a correct guess, what number would have the highest probability of winning? Please explain your reasoning.

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