
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 19th Asian Games will be held in Hangzhou, China on September 23, 2023, with esports being included as an official competition for the first time. A certain high school conducted a survey among male and female students to determine their interest in esports. They randomly surveyed 200 male and 200 female students and obtained the following data:

|         | Male  | Female | Total |
|---------|-------|--------|-------|
| Like    | 120   | 100    | 220   |
| Dislike | 80    | 100    | 180   |
| Total   | 200   | 200    | 400   |

$(1)$ Based on the data in the table, using a significance level of $\alpha = 0.05$ for the independence test, can it be concluded that the students' interest in esports is related to their gender?  
$(2)$ To understand the reasons why students do not like esports, a stratified sampling method is used to randomly select 9 students who do not like esports. From these 9 students, 3 are selected for face-to-face communication. Find the probability of "at least one male student being selected."  
$(3)$ Considering frequencies as probabilities and using samples to estimate the population, 10 students are randomly selected from all students in the school. Let $X$ be the number of students who like esports among the 10 selected students. Find the expected value of $X$.

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

| $\alpha$ | 0.15  | 0.10  | 0.05  | 0.025 | 0.01  |
|----------|-------|-------|-------|-------|-------|
| $x_{\alpha}$ | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 |

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