
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 school organized a trip for 1 teacher and 6 students to three cities, A, B, and C, during the summer vacation. Each city will have 2 students assigned randomly, and the teacher can choose any city. Let event A be "student a and the teacher go to the same city," and event B be "students a and b go to the same city."
(1) Find the probabilities of events A and B, denoted as P(A) and P(B);
(2) Let $\xi$ denote the total number of occurrences of events A and B in one arrangement. Find the expected value of the random variable $\xi$, denoted as $E\xi$.

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