
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
During the review class for the midterm exam, the teacher presented a probability problem that was to be solved independently by three students: A, B, and C. The probabilities of each solving the problem were $\frac{1}{5}$, $\frac{1}{4}$, and $\frac{1}{3}$, respectively, and their success in solving the problem was independent of each other.  
(1) Calculate the probability that exactly two of them solve the problem.  
(2) Which is greater, the probability that the problem is solved or the probability that it is not solved? Please explain your reasoning.

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