
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
The $18$th Asian Cup will be held in Qatar on January 12, 2024, and is expected to attract millions of fans to watch. In order to understand whether the preference for watching football matches among university students is related to gender, the university news station randomly selected $100$ students for a survey. Among them, the proportion of female students who enjoy watching football matches is $\frac{1}{4}$ of the total number of female students, and $10$ male students indicated that they do not like watching football matches. 

$(1)$ Complete the $2\times 2$ contingency table below. Based on the small probability value $\alpha = 0.001$, conduct an independence test to determine whether the preference for watching football matches is related to gender.

\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Male} & \text{Female} & \text{Total} \\
\hline
\text{Enjoy watching football} & & & \\
\hline
\text{Do not enjoy watching football} & & & \\
\hline
\text{Total} & 60 & & \\
\hline
\end{array}
\]

$(2)$ Among the audience who do not enjoy watching football, $8$ people are selected using stratified random sampling by gender. From these $8$ people, $2$ are randomly selected to participate in the school news station's interview program. Let the number of male students selected be $X$. Find the probability distribution and expectation of $X$.

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

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\alpha & 0.1 & 0.05 & 0.01 & 0.005 & 0.001 \\
\hline
x_{\alpha} & 2.706 & 3.841 & 6.635 & 7.879 & 10.828 \\
\hline
\end{array}
\]

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