
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
In a box, there are three cards labeled $1, 2, 3$. Two cards are drawn sequentially with replacement, labeled as $x$ and $y$. Let $\xi = |x-2| + |y-x|$.
(1) Find the maximum value of the random variable $\xi$ and the probability of the event where $\xi$ attains its maximum value.
(2) Find the probability distribution and the expected value of the random variable $\xi$.

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