
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 teacher of course $A$ at a certain university conducted a random survey of some information about 200 students who chose to take this course this semester. The specific data is shown in the table below:

|          | Major in this field | Major not in this field | Total |
|----------|----------------------|-------------------------|-------|
| Female   | 70                   |                         | 80    |
| Male     |                      | 40                      |       |
| Total    |                      |                         |       |

$(1)$ Complete the $2\times 2$ contingency table based on the known conditions and determine whether there is a $99.9\%$ certainty that the choice of course $A$ by students is related to whether they are majoring in this field and their gender.

$(2)$ From the sample of students majoring not in this field, first use stratified sampling method based on gender ratio to select 5 people, then randomly select 3 people from these 5 people. Find the probability that all 3 people are male.

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

| $P(K^{2}\geqslant k_{0})$ | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
|---------------------------|------|------|-------|-------|-------|-------|
| $k_{0}$                   | 2.706| 3.841| 5.024 | 6.635 | 7.879 | 10.828|

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