
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 fair six-sided die is rolled twice in succession and lands on a horizontal table. Let $x$ and $y$ represent the numbers facing up on the first and second roll, respectively. Define event $A$ as "$x \cdot y$ is even", and event $B$ as "both $x$ and $y$ are even". Calculate the conditional probability $P(B \mid A)$.

A) $\frac{1}{2}$
B) $\frac{1}{4}$
C) $\frac{3}{10}$
D) $\frac{1}{3}$

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