
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
The 2010 Shanghai World Expo in China officially opened on May 1, 2010, in Shanghai. One day, Mr. Wang took a train from Chongqing to Shanghai to visit the Expo. Assuming that the probabilities of three trains from Chongqing to Shanghai arriving on time are $0.8$, $0.7$, and $0.9$ respectively, and also assuming that the punctuality of these trains is independent of each other, determine:
(1) The probability that exactly two of the three trains arrive on time.
(2) The probability that at least one of the three trains arrives on time.

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