
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
Driving while using a mobile phone is illegal and poses a serious safety hazard, endangering the lives of both the driver and others. In order to study the situation of drivers using mobile phones while driving, the traffic police randomly surveyed 100 drivers and obtained the following statistics: among 55 male drivers, 40 of them use a phone while driving and 15 do not; among 45 female drivers, 20 use a phone while driving and 25 do not.  
$(1)$ Complete the $2\times 2$ contingency table below and determine whether there is a $99.5\%$ confidence that using a phone while driving is related to the driver's gender:  
|                  | Using Phone while Driving | Not Using Phone while Driving | Total |
|------------------|----------------------------|--------------------------------|-------|
| Male Drivers     |                          |                              |       |
| Female Drivers   |                          |                              |       |
| Total            |                          |                              |       |  

$(2)$ Using stratified sampling, select 8 people who do not use a phone while driving, then randomly select 3 people from these 8. Let $X$ be the number of male drivers who do not use a phone while driving. Find the distribution table and the expected value of $X$.  
Reference data:  
| $P(K^{2} > k_{0})$ | $0.15$ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|---------------------|--------|--------|--------|---------|---------|---------|---------|
| $k_{0}$            | $2.072$ | $2.706$ | $3.841$ | $5.024$ | $6.635$ | $7.879$ | $10.828$ |  
Reference formula:  
$K^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.

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