
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
It is known that there is a four-person team consisting of boys A and B and girls C and D participating in a quiz activity organized by a TV station. The activity consists of four rounds. Let the probabilities for the boys to pass rounds one to four be $\frac{5}{6}, \frac{4}{5}, \frac{3}{4}, \frac{2}{3}$, respectively, and the probabilities for the girls to pass rounds one to four be $\frac{4}{5}, \frac{3}{4}, $\frac{2}{3}, \frac{1}{2}$, respectively.
(1) Find the probability that a boy passes all four rounds;
(2) Let $\xi$ represent the number of people in the four-person team who pass all four rounds. Find the distribution and the expectation of the random variable $\xi$.

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