
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 certain examination, suppose the probabilities of candidates A, B, and C passing are respectively $\frac{2}{5}$, $\frac{3}{4}$, and $\frac{1}{3}$, and the events of each passing are mutually independent.
(1) Find the probability that all three candidates pass;
(2) Find the probability that at least one candidate passes;
(3) Which event of passing is most likely to occur?

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