
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 order to understand whether employees' hobbies are related to gender, a research unit randomly selected 100 male and female employees in the unit to conduct a questionnaire survey. The following contingency table was obtained:

|         | Male | Female | Total |
|---------|------|--------|-------|
| Hobby   | 30   |        |       |
| No Hobby|      | 10     |       |
| Total   |      |        | 100   |

$(1)$ Please complete the above contingency table and analyze whether the hobby of exercising is related to gender based on an independence test with a small probability value of $\alpha = 0.01$;  
$(2)$ If 2 people who do not like to exercise are randomly selected from these 100 people to participate in sports training, let the number of males selected be $X$. Find the distribution table and mathematical expectation of $X$.  
Reference:  
| $\alpha$ | 0.1   | 0.05  | 0.01  | 0.005 | 0.001  |
|----------|-------|-------|-------|-------|--------|
| $x_{\alpha}$ | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |

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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