
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
From February 4th to February 20th, 2022, the 24th Winter Olympic Games will be held in Beijing and Zhangjiakou. In order to understand whether college students are interested in curling, a research institution randomly selected 600 people from a university for a survey. It was found that the ratio of male to female participants was 2:1. Two-thirds of the total number of participants were interested in curling, and 50 female participants were not interested in curling. 

$(1)$ Complete the $2\times 2$ contingency table below and determine whether there is a 99.9% confidence that interest in curling is related to gender.

\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Interested} & \text{Not Interested} & \text{Total} \\
\hline
\text{Male} & & & \\
\hline
\text{Female} & & 50 & \\
\hline
\text{Total} & & & 600 \\
\hline
\end{array}
\]

$(2)$ Using stratified sampling by gender, 8 students interested in curling were randomly selected. If 2 students are randomly chosen from these 8 to be curling promoters, find the probability that at least one of the 2 selected students is female.

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

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
P(K^{2}\geqslant k_{0}) & 0.100 & 0.050 & 0.025 & 0.010 & 0.001 \\
\hline
k_{0} & 2.706 & 3.841 & 5.024 & 6.635 & 10.828 \\
\hline
\end{array}
\]

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