
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]


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In a certain physics exam, the scores $\xi$ follow a normal distribution, i.e., $\xi \sim N(70, 100)$. The full score is 100 points.
(1) Try to find the probability that the exam score $\xi$ falls within the interval (50, 90).
(2) If there are 1000 students taking this exam, estimate the number of students who pass the exam (score at least 60 points).
(Note: If $\xi \sim N(\mu, \sigma^2)$, then $P(\mu-\sigma < \xi < \mu+\sigma) = 0.6826$, $P(\mu-2\sigma < \xi < \mu+2\sigma) = 0.9544$, $P(\mu-3\sigma < \xi < \mu+3\sigma) = 0.9974$)

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