
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
(14 points)  
There are two bus services, A and B, from location A to location B in one day. Due to the influence of rainy and snowy weather, over a period, the probability of bus A arriving on time at location B is 0.7, and the probability of bus B arriving on time at location B is 0.75.  
(1) Three tourists take bus A on three different days from location A to location B. Calculate the probability that exactly two of them arrive on time.  
(The answer should be expressed as a number.)  
(2) Two tourists take buses A and B, respectively, from location A to location B. Calculate the probability that at least one of them arrives on time.  
(The answer should be expressed as a number.)

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