
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
Given two dice are thrown in succession, with the six faces of each die labeled with $1$, $2$, $3$, $4$, $5$, and $6$ points, let event $A$ be "$x+y$ is odd" and event $B$ be "$x$, $y$ satisfy $x+y<6$, where $x$ and $y$ are the numbers of points facing up on the two dice when they land on a tabletop. Calculate the conditional probability $P(B|A)$.

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