
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
Peter and 9 other people are playing a game where each person rolls a die. A player wins a prize if they roll a number that no one else rolls.

a) (For grades 6 - 11, 1 point) What is the probability that Peter wins a prize?

b) (For grades 8 - 11, 3 points) What is the probability that at least one person wins a prize?

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