
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 certain grade has 2000 students. The scores of a physics unit test approximately follow a normal distribution $X\sim N(72, 8^{2})$.  
$(1)$ Find the proportion of students whose scores do not exceed 64 points out of the total number of students in the grade.  
$(2)$ Estimate the number of students in the entire grade with scores between 80 and 96 points.  
Given: If $X\sim N(\mu, \sigma^{2})$, then $P(\mu - \sigma \leq X \leq \mu + \sigma) \approx 0.6827$, $P(\mu - 2\sigma \leq X \leq \mu + 2\sigma) \approx 0.9545$, $P(\mu - 3\sigma \leq X \leq \mu + 3\sigma) \approx 0.9973$.

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