
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
In a diagnostic math test for high school seniors at a certain school, the scores (in points) follow a normal distribution $N(100, 10^{2})$. Let $X$ be the score of a randomly selected student. Let event $A$ be defined as the student's score being $80 < X \leqslant 100$, and event $B$ be defined as the student's score being $70 < X \leqslant 90$. Find the conditional probability of event $B$ given that event $A$ has occurred, denoted as $P(B|A)=\_\_\_\_\_\_$ (express the result as a fraction). 

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

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