
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
Roll a die (with faces numbered 1, 2, 3, 4, 5, 6) twice in succession, and let the numbers on the faces that land facing up be $x$ and $y$, respectively. Define event A as "the sum of $x$ and $y$ is an even number", and event B as "one of $x$ or $y$ is an even number and $x \neq y$". Then, the probability $P(B|A) = \_\_\_\_\_\_$.

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