
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
In response to the call for energy conservation and environmental protection, a car manufacturing company has independently developed an electric car. They now want to study the speed of ordinary household cars on highways. By using relevant data from the transportation department, a survey was conducted on 100 household car drivers. The survey results showed that among 55 male drivers, 40 of them had an average speed exceeding 100 km/h, and 15 did not. Among 45 female drivers, 20 had an average speed exceeding 100 km/h, and 25 did not. 

$(1)$ Complete the contingency table below and determine whether there is a $99.5\%$ confidence that the average speed exceeding 100 km/h is related to gender.

|                  | Number of Drivers with Average Speed > $100$ km/h | Number of Drivers with Average Speed $\leq 100$ km/h | Total |
|------------------|--------------------------------------------------|------------------------------------------------------|-------|
| Male Drivers     |                                                  |                                                      |       |
| Female Drivers   |                                                  |                                                      |       |
| Total            |                                                  |                                                      |       |

$(2)$ Using the sample data above to estimate the population, randomly select 3 cars from a large number of household cars on the highway. Let $X$ be the number of cars among the 3 selected cars driven by males with speeds exceeding 100 km/h. If the results of each selection are independent, find the distribution table and the expected value of $X$.

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

| $P(K^{2}\geqslant k_{0})$ | $\ldots $ | $0.25$ | $0.15$ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $\ldots $ |
|---------------------------|-----------|--------|--------|--------|--------|---------|---------|---------|----------|
| $k_{0}$                  | $\ldots $ | $1.323$| $2.072$| $2.706$| $3.841$| $5.024$ | $6.635$ | $7.879$ | $\ldots $ |

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