
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 company uses a testing method to recruit talents. Candidates must choose any two out of three test locations B, C, and D to take tests. If a candidate passes the tests at both chosen locations, they are eligible for an interview; otherwise, they will not be hired. The results at each test location are binary, either pass or fail, with independent outcomes for each location. Candidate Xiao Li has a probability of passing at test locations B, C, and D of $\frac{2}{3}$, $\frac{1}{3}$, and $\frac{1}{2}$ respectively, while candidate Xiao Wang has a passing probability of $\frac{2}{3}$ for all three test locations.
(Ⅰ) Which two test locations should Xiao Li choose to maximize the probability of being eligible for an interview? Please explain your reasoning.
(Ⅱ) Suppose Xiao Li chooses test locations B and C, while Xiao Wang chooses B and D. Let $\xi$ be the sum of the number of test locations at which both pass. Determine the probability distribution and the expected value $E\xi$ of the random variable $\xi$.

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