
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
Exercise for an hour every day, live a healthy life for a lifetime. Nowadays, many young people are in a "sub-healthy" state due to various reasons. In order to understand the current exercise status of young people, a certain social institution conducted a survey, randomly interviewed 100 young people, and statistically analyzed the results of their surveys, dividing them into male group and female group. Young people who exercise for at least 5 hours per week are classified as "healthy living," while those who exercise less than 5 hours are classified as "sub-healthy living." A $2 \times 2$ contingency table was drawn based on the survey results.

|         | Healthy Living | Sub-healthy Living | Total |
|---------|----------------|--------------------|-------|
| Male    | 30             | 45                 | 75    |
| Female  | 15             | 10                 | 25    |
| Total   | 45             | 55                 | 100   |

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

| $P(K^{2}\geqslant k_{0})$ | $0.050$ | $0.010$ | $0.001$ |
|---------------------------|---------|---------|---------|
| $k_{0}$                   | $3.841$ | $6.635$ | $10.828$|

$(1)$ Can we be $95\%$ confident that whether "healthy living" is related to the gender of young people? (Round the calculation result to three decimal places)<br/>
$(2)$ Using stratified sampling, select 6 out of the 45 young people living a healthy life to participate in a charity event. Two of these 6 young people need to be randomly selected as contact persons for the event. Find the probability that both contact persons are male.

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