
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
Freshman Xiao Wang took an elective course named "Teaching and Life," which assesses students through both theoretical and social practice examinations. Each part of the assessment is graded as either "Pass" or "Fail," and only students who pass both parts can earn credits for the course. The probabilities of passing the theoretical examination for students A, B, and C are $\frac{5}{6}$, $\frac{4}{5}$, and $\frac{3}{4}$, respectively, while the probabilities of passing the social practice examination are $\frac{1}{2}$, $\frac{2}{3}$, and $\frac{5}{6}$, respectively. The outcomes of the assessments are independent of each other.  
(1) Assuming A, B, and C simultaneously undergo both the theoretical and social practice assessments, who has the highest probability of earning the course credits;  
(2) Calculate the probability that exactly two out of these three students earn the course credits after undergoing both assessments.

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