
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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Three students, A, B, and C, participate in a self-recruitment exam held by a university. The exam consists of two rounds: a written test and an interview. Only those who pass the written test can proceed to the interview round. Passing the interview grants the students an advantage in the university's admission process. The written test and interview are independent of each other. Based on past mock tests, the probabilities of A, B, and C passing the written test are 0.4, 0.8, and 0.5, respectively, and the probabilities of passing the interview are 0.8, 0.4, and 0.64, respectively. Based on this data, we can predict:

1. The probability that at least two of the three students pass the written test.
2. The mathematical expectation of the number of students (X) among A, B, and C who will receive the university's admission advantage.

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