
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
A game involves rolling a die. If a 1, 2, or 3 is rolled, the player earns 1 point. If a 4 or 5 is rolled, the player earns 2 points. If a 6 is rolled, the player earns 3 points.  
(1) Calculate the expected score for student A after one roll.
(2) Students A and B each roll the die twice, obtaining scores $x$ and $y$ respectively. Calculate the probability that $|x-y| \geq 1$.

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