
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 the movie "The Wandering Earth," there is a classic line: "There are millions of roads, safety comes first," reminding drivers to consciously abide by the traffic safety regulations. When encountering pedestrians crossing the pedestrian crossing, drivers should stop and give way to pedestrians. The traffic police department of a city randomly selected 100 drivers passing through the main road intersection to investigate the relationship between the behavior of "not giving way to pedestrians" and driving experience. The results are shown in the table below:

|                  | No "Not Giving Way" | With "Not Giving Way" | Total |
|------------------|---------------------|-----------------------|-------|
| Driving experience less than 2 years | 8 | 2 | 10 |
| Driving experience more than 2 years | 60 | 30 | 90 |
| Total | 68 | 32 | 100 |

$(1)$ Can it be concluded with 90% confidence that the behavior of "not giving way to pedestrians" is related to driving experience?  
$(2)$ Considering frequency as probability, now randomly select 3 drivers with more than 2 years of driving experience. Let $X$ be the number of the 3 selected drivers who do not exhibit the behavior of "not giving way to pedestrians." Find the distribution table and mathematical expectation of $X$.

Given critical value table:

| $k$ | $0.10$ | $0.05$ | $0.010$ |
|-----|--------|--------|---------|
| $P(\chi ^{2} \gt k)$ | $2.706$ | $3.841$ | $6.635$ |

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

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