
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 major food hygiene inspection, law enforcement officers learned from sampling that the current pass rates of two types of food, A and B, in our city are 90% and 80%, respectively.  
(1) If three students gather and each randomly selects one item from both types of food, what is the probability that exactly one student gets two items that are both unqualified?  
(2) If a consumer randomly purchases one item from each of the two types of food, and $\xi$ represents the number of unqualified food items purchased, find the expected value of $\xi$.

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