
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 person A and a person B participate in an English exam. It is known that out of the 10 available questions, A can answer 6 correctly and B can answer 8 correctly. Each exam consists of a random selection of 3 questions from the available 10 questions. To pass the exam, a person must answer at least 2 questions correctly.
1. Find the probability distribution and the mathematical expectation for the number of questions A answers correctly, $\xi$.
2. Find the probability that at least one of A or B passes the exam.

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