
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 mathematics test consisting of 10 multiple-choice questions, each with 4 options and only one correct answer, the scoring criteria are as follows: 5 points for a correct answer, and 0 points for a wrong answer or no answer. A student gave an answer for each question. It is known that the student answered 6 questions correctly. Among the remaining questions, the student could eliminate two wrong options for two questions, eliminate one wrong option for another question, and had to guess on one question due to a lack of understanding. Calculate the probability that the student scores:
(I) 45 points,
(II) the expected value of the score ξ.

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