
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
The new college entrance examination reform in Inner Mongolia Autonomous Region has been implemented since 2022. After canceling the classification of arts and sciences, the "$3+1+2$" mode is adopted, that is, Chinese, mathematics, and English are national unified examinations that all candidates must take. Then, one subject is selected from physics and history, and two subjects are selected from chemistry, biology, politics, and geography to participate in the college entrance examination. Before selecting subjects, it is generally believed that the traditional "big arts and big sciences" (i.e., "mathematics and physics," "politics, history, and geography" combination) is still mainstream, and male students will still be the main group for "big sciences." A school, in order to understand whether students' choices of "big sciences" are related to gender, randomly sampled 100 students (55 male students and 45 female students) from the first year of high school, and found that the number of students choosing "big sciences" is 20 more than those choosing non-"big sciences."

$(1)$ Complete the $2\times 2$ contingency table above and determine whether it can be considered that the choice of "big sciences" is related to gender under the premise that the probability of making an error does not exceed $0.5\%$.

$(2)$ To further understand the reasons for students' subject choices, four male students and two female students were randomly selected for interviews, and two representatives were selected for detailed discussions. Find the probability of selecting at least one female student.

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

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