
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
One day, Xiao Wang took a train from Chongqing to Shanghai for business. If the probabilities of three trains arriving on time from Chongqing to Shanghai on that day are $0.8$, $0.7$, and $0.9$ respectively, assuming that the punctuality of these three trains does not affect each other. Find:<br/>$(1)$ The probability that exactly two of these three trains arrive on time;<br/>$(2)$ The probability that at least one of these three trains arrives on time.

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