
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
In a math competition, there were 6 different questions. Each student randomly selected 3 questions to answer. It is known that student A could correctly answer 4 of the 6 questions, while student B had a probability of $\frac {2}{3}$ of correctly answering each question. The answers of students A and B were independent and did not affect each other.

1. Calculate the probability that students A and B together correctly answer 3 questions.
2. If students A and B correctly answered m and n questions respectively, and since student A's class had one less participant, each correct answer from student A is worth 15 points, while each correct answer from student B is worth 10 points. Calculate the expected value of the total score X of students A and B.

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