
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
After a survey in a city, a school analyzed the math test scores of two liberal arts classes, class A and class B. It was stipulated that scores greater than or equal to $120$ points are excellent, and scores below $120$ points are not excellent. After the scores were counted, the school obtained the following contingency table. It is known that out of a total of $110$ students in classes A and B, $30$ students are excellent.
$(1)$ Please complete the contingency table below:
```
|         | Excellent | Not Excellent | Total |
|---------|-----------|---------------|-------|
| Class A |    $10$   |               |       |
| Class B |           |     $30$      |       |
| Total   |           |               | $110$ |
```
$(2)$ Based on the data in the contingency table, can we conclude that "scores are related to classes" with a $99.9\%$ confidence level?
$(3)$ From the number of "not excellent" students in classes A and B, $8$ students are randomly selected from each class. How many students are selected from classes A and B respectively?
Reference formula and critical value table: ${χ^2}=\frac{{n{{(ad-bc)}^2}}}{{(a+b)(c+d)(a+c)(b+d)}}$
```
| $P(\chi ^{2}\geqslant \alpha )$ | $0.100$ | $0.050$ | $0.025$ | $0.010$ | $0.001$ |
|----------------------------------|---------|---------|---------|---------|---------|
| $\alpha $                        | $2.706$| $3.841$| $5.024$| $6.635$| $10.828$|
```

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