
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
Person A and person B each guess a riddle in each guessing activity. If one person guesses correctly and the other person guesses incorrectly, the person who guessed correctly wins; otherwise, it is a tie. It is known that in each activity, the probabilities of A and B guessing correctly are $\frac{5}{6}$ and $\frac{3}{5}$, respectively. The outcomes of A and B guessing correctly or incorrectly do not affect each other within each activity, and each activity is independent of others. The probability of A winning in one activity is ______; the probability of A winning at least 2 out of 3 activities is ______.

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