
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
To investigate the myopia situation of students, a certain region selected 500 students from two schools, School A and School B, in different geographical environments to participate in the survey. The survey results are divided into two categories: "myopia" and "non-myopia," and the results are as shown in the table below:

|           | Number of Myopic Students | Number of Non-Myopic Students | Total |
|-----------|---------------------------|-------------------------------|-------|
| School A  | 250                       | 250                           | 500   |
| School B  | 300                       | 200                           | 500   |
| Total     | 550                       | 450                           | 1000  |

$(1)$ Estimate the frequency of myopia for students in School A and School B, respectively.  
$(2)$ Based on the survey data, can we be 99% confident that the number of myopic students is related to the different geographical environments of the schools?  
Given: $K^2 = \frac{n(ad-bc)^2}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.

| $P(K^{2}\geqslant k)$ | $0.050$ | $0.010$ | $0.001$ |
|-----------------------|---------|---------|---------|
| $k$                   | $3.841$ | $6.635$ | $10.828$ |

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