
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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A total of 1000 students from a certain school took a math test. The test scores $\xi$ are approximately normally distributed as $N(110, \sigma^2)$. If $P(110 \leqslant \xi \leqslant 130) = 0.35$, estimate the number of students who scored below 90 (failed).

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