
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
Two individuals, A and B, each draw one ticket from a set of 3 lottery tickets, where one is a first-prize ticket, one is a second-prize ticket, and the remaining ticket is a non-winning ticket. Determine the probability that exactly one person wins a prize.

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