
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
"Using animals for medical experiments is correct, as it can save human lives." An organization conducted a random survey of 200 adults in a certain city to understand their attitudes towards this statement (attitudes are categorized as agree or disagree). The data obtained is as follows:

|         | Male | Female | Total |
|---------|------|--------|-------|
| Agree   | 70   | 50     | 120   |
| Disagree| 30   | 50     | 80    |
| Total   | 100  | 100    | 200   |

$(1)$ Can we be $99\%$ confident that adults' attitudes towards this statement are related to gender?  
$(2)$ Considering frequencies as probabilities, estimate the population from the sample. If 3 people are randomly selected from the adults in the city to understand their attitudes towards this statement, let $X$ be the number of people who agree. Find the distribution table and the expected value of $X$.  
Given: ${\chi^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$, and the table below:

| $P(\chi^2 \geq x_0)$ | $0.025$ | $0.010$ | $0.005$ |
|----------------------|---------|---------|---------|
| $x_0$                | $5.024$ | $6.635$ | $7.879$ |

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