
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
A certain type of beverage with a prize promotion has bottle caps printed with either "reward one bottle" or "thank you for your purchase". If a bottle is purchased and the cap is printed with "reward one bottle", it is considered a winning bottle, with a winning probability of $\frac{1}{6}$. Three students, A, B, and C, each bought a bottle of this beverage.

1. Find the probability that none of the three students win a prize.
2. Find the probability that at least two of the three students do not win a prize.

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