
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 game is composed of the following rules:

i) In each round, a standard fair die is rolled.

ii) If the number 3 comes up, then player $A$ wins.

iii) If a number from the set $\{4, 5, 6\}$ comes up, then player $B$ wins.

iv) If a number from the set $\{1, 2\}$ comes up, then the die is rolled again until resulting in 3, 4, 5, or 6.

What is the probability that player $B$ wins?

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