
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 senior high school student's math diagnostic test scores $X$ follow a normal distribution $N(110, 10^2)$. When selecting a student's math score $\xi$, define event $A$ as $90 < \xi \leqslant 110$, and event $B$ as $80 < \xi \leqslant 100$. Find the probability of event $B$ occurring given that event $A$ has occurred, denoted as $P(B|A)=$ ______ (express the answer as a fraction).

Note: $X$ satisfies $P(\mu-\sigma < X \leqslant \mu+\sigma)=0.68$, $P(\mu-2\sigma < X \leqslant \mu+2\sigma)=0.95$, and $P(\mu-3\sigma < X \leqslant \mu+3\sigma)=0.99$.

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