
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 pocket, there are eight cards of the same size, of which three are labeled with the number 1, three with the number 2, and two with the number 3. One card is drawn at random, replaced, and then a second card is drawn at random. Let the random variable $\xi$ denote the sum of the numbers on the two cards drawn.  
(I) For what value of $\xi$ is the probability of occurrence the highest? Explain the reasoning.  
(II) Calculate the expected value $E(\xi)$ of the random variable $\xi$.

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