
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
In a prize-winning beverage sale, the bottle cap is printed with either "Reward one bottle" or "Thank you for your purchase". Buying a bottle and finding a "Reward one bottle" message under the cap indicates a win with a probability of $\frac{1}{6}$. Three students, A, B, and C, each buy one bottle of the beverage.
(I) Calculate the probability that all three students do not win.
(II) Calculate the probability that at least two out of the three students do not win.

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