
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 recent years, the rate of poor eyesight among Chinese primary and secondary school students has been continuously increasing. A research team speculates that this may be related to students frequently using electronic devices. To verify the reasonableness of this speculation, the team conducted a questionnaire survey on a class, and the survey data is shown in the table below.

| Time of Using Electronic Devices Daily | Eyesight Condition |
|---------------------------------------|--------------------|
|                                      | Nearsighted        | Not Nearsighted   |
| Over 1 hour                           | 35                 | 5                  |
| Not more than 1 hour                   | 5                  | 5                  |

$(1)$ Can we be $99\%$ certain that there is a relationship between students being nearsighted and using electronic devices for more than $1$ hour per day?

$(2)$ Estimate the probability by frequency. One student is randomly selected from the entire school for an interview, and it is known that the student is nearsighted. Find the probability that the student uses electronic devices for not more than $1$ hour per day.

$(3)$ Estimate the probability by frequency. Five students are randomly selected from the entire school for interviews. Find the probability that exactly $2$ of the students are nearsighted.

Given: ${K}^{2}=\frac{n{(ad-bc)}^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $a+b+c+d=n$.

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

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