
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 school established a soccer club to enrich students' extracurricular activities. In order to determine if students' preference for soccer is related to gender, $100$ male and $100$ female students were randomly selected for a survey. Some of the data is shown in the table below:

|         | Likes Soccer | Does Not Like Soccer | Total |
|---------|--------------|----------------------|-------|
| Boys    |              | $40$                 |       |
| Girls   | $30$         |                      |       |
| Total   |              |                      |       |

$(1)$ Complete the table above based on the given data. According to the independence test with $\alpha = 0.001$, can it be concluded that students' preference for soccer at this school is related to gender?  
$(2)$ The club's coach selected $2$ male students and $1$ female student who like soccer to demonstrate penalty kicks. It is known that the probability of scoring a goal for each of the two male students is $\frac{2}{3}$, and for the female student is $\frac{1}{2}$. Assuming each person takes one shot independently, find the distribution and the expected value of the total number of goals $X$ scored by the $3$ students.  
Given: ${\chi^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$.  
| $\alpha $ | $0.1$ | $0.05$ | $0.01$ | $0.005$ | $0.001$ |
|-----------|-------|--------|--------|---------|---------|
| $x_{\alpha }$ | $2.706$ | $3.841$ | $6.635$ | $7.879$ | $10.828$ |

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