
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
A course assessment consists of two parts: theory and experiment. Each part is graded as either "pass" or "fail". If a student passes both parts, they pass the course. Students A, B, and C have probabilities of 0.6, 0.5, and 0.4 respectively to pass the theory part, and probabilities of 0.5, 0.6, and 0.75 respectively to pass the experiment part. The pass/fail status of each part is independent of the others.

1. Calculate the probability that at least two of the students A, B, and C pass the theory part.
2. Calculate the probability that all three students pass the course.

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