
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]


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A, B, and C, three students, jointly participate in an autonomous recruitment exam organized by a university, which includes both a written and an oral component. Those who pass both parts will become pre-admitted students of the university (and can be admitted with bonus points in the college entrance examination). The two exam parts are independent of each other. According to the analysis of A, B, and C's usual academic performance, the probabilities for A, B, and C to pass the written exam are 0.6, 0.5, and 0.4, respectively, and to pass the oral exam are 0.5, 0.6, and 0.75, respectively.

(1) Calculate the probability that exactly one student among A, B, and C passes the written exam;
(2) Let the random variable ξ denote the number of students who could be pre-admitted by the university after the two exams. Calculate the expected value E(ξ).

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