
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
A certain survey agency conducted an online questionnaire to investigate whether the use of a product is related to gender. They randomly selected $50$ responses for analysis and obtained the following $2\times 2$ contingency table:

|         | Male | Female | Total |
|---------|------|--------|-------|
| Use     | $15$ | $5$    | $20$  |
| Not Use | $10$ | $20$   | $30$  |
| Total   | $25$ | $25$   | $50$  |

$(1)$ Based on the survey results, analyze how confident you are that the use of the product is related to gender.  
$(2)$ Among those who do not use the product, $6$ people are selected using stratified sampling by gender. From these $6$ people, $2$ are randomly selected to participate in an activity. Let $X$ be the number of females selected to participate in the activity. Find the probability distribution and the expected value of $X$.  
Given: $K^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$.  

| $P(K^{2}\geqslant k)$ | $0.010$ | $0.005$ | $0.001$ |
|-----------------------|---------|---------|---------|
| $k$                   | $6.635$ | $7.879$ | $10.828$ |

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