
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
During a swimming competition at a sports meet, it is known that 1 out of 5 swimmers has taken a stimulant, which is to be determined through urine testing. A positive urine test result indicates the use of stimulants, while a negative result means no stimulants were used. The organizing committee provides two testing methods:
Scheme A: Test each athlete individually until the one who used stimulants is identified.
Scheme B: First, select any 3 athletes and test their urine mixed together. If the result is positive, it indicates that one of these 3 athletes used stimulants, and then test each one individually until the one who used stimulants is identified. If the result is negative, then select and test one of the remaining 2 athletes.
(Ⅰ) Find the probability that the number of tests required by scheme A is not less than the number required by scheme B.
(Ⅱ) Let ξ denote the number of tests required by scheme B. Calculate the expected value of ξ.

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