
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
As the New Year's Day of 2024 approaches, domestic films and Hollywood blockbusters from abroad will be released simultaneously. The majority of netizens will vote for their favorite movies. A platform randomly selects 200 people from all viewers to conduct a survey on the audience's movie preferences. The data is shown in the table below (unit: people):
$(1)$ Complete the $2\times 2$ contingency table and analyze whether the movie preferences are related to gender based on an independence test with a small probability value of $\alpha = 0.005$;
$(2)$ If the frequencies are considered as probabilities, randomly select 3 people from the audience who chose "domestic" out of the 200 people. Let the random variable $X$ represent the number of female viewers selected. Find the distribution table and the expected value of $X$.

|         | Domestic | Foreign | Total |
|---------|----------|---------|-------|
| Male    |          | 40      | 100   |
| Female  | 80       |         |       |
| Total   |          |         | 200   |

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

| $\alpha $ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|-----------|--------|--------|---------|---------|---------|---------|
| $x_{\alpha }$ | $2.706$ | $3.841$ | $5.024$ | $6.635$ | $7.879$ | $10.828$ |

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