
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]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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system
Before a vaccine is put on the market, it must undergo strict testing and obtain relevant data through clinical trials to ensure the safety and effectiveness of the vaccine. A biological product research institute used a certain type of vaccine on laboratory mice for scientific research and clinical trials, obtaining the following statistical data:

|                  | Not Infected with Virus | Infected with Virus | Total |
|------------------|-------------------------|---------------------|-------|
| Not Vaccinated   | 40                      | p                   | x     |
| Vaccinated       | 60                      | q                   | y     |
| Total            | 100                     | 100                 | 200   |

Now, one laboratory mouse is randomly selected from those not vaccinated, and the probability of selecting a mouse infected with the virus is $\frac{3}{5}$.
- (1) Find the values of p, q, x, and y in the 2x2 contingency table.
- (2) Is there a 95% confidence that this vaccine is effective? Explain your reasoning.
- (3) Among the mice infected with the virus, a sample of 10 mice is selected based on the ratio of not vaccinated to vaccinated mice (3:2). Then, 4 mice are randomly selected from these 10 mice for verification of vaccination status. Let X be the number of mice among the 4 that were not vaccinated. Find the distribution of X and its expected value $E(X)$.

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

| $P(\chi ^{2}\geqslant k)$ | 0.10 | 0.05 | 0.01 | 0.005 | 0.001 |
|---------------------------|------|------|------|-------|-------|
| $k$                       | 2.706| 3.841| 6.635| 7.879 | 10.828|

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