
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 Qingming Festival holiday, it is known that the probability of student A visiting Wuyuan Ancient Town is $\frac{2}{3}$, the probability of student B visiting Wuyuan Ancient Town is $\frac{1}{4}$, and the probability of student C visiting Wuyuan Ancient Town is $\frac{2}{5}$. Moreover, the actions of students A, B, and C do not affect each other.  
(1) Calculate the probability of students A, B, and C all visiting Wuyuan Ancient Town during the Qingming Festival holiday.  
(2) Calculate the probability of only one among students A, B, and C visiting Wuyuan Ancient Town during the Qingming Festival holiday.

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