
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]


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The $22^{nd}$ FIFA World Cup was held in Qatar from November 20th to December 18th, 2022, causing a global football craze. In order to properly conduct football courses, a certain middle school randomly selected 60 male students and 40 female students for a survey. The results are as follows: the number of people who answered "do not like" accounts for $\frac{2}{5}$ of the total number of people. Among those who answered "like," the number of female students is $\frac{1}{3}$ of the number of male students.  
$(1)$ Please fill in the $2\times 2$ contingency table below based on the above data, and based on this, determine whether there is a $99.9\%$ certainty that students' preference for football is related to gender.  

| Gender | Preference for Football | Dislike Football | Total |
|--------|--------------------------|------------------|-------|
| Female |                        |                  |       |
| Male   |                        |                  |       |
| Total  |                        |                  |       |

$(Ⅱ)$ Consider the proportions of male and female students who like football in the above survey as probabilities. A survey of a certain class in the school found that the number of students who like football accounts for $\frac{33}{56}$ of the total number of students. Estimate the proportion of female students in this class.  
Given: $\chi ^{2}=\frac{n(ad-bc)^2}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.  

|$P(\chi ^{2}\geqslant x_{0})$| $0.1$ | $0.05$ | $0.01$ | $0.005$ | $0.001$ |
|-----------------------------|--------|--------|--------|---------|---------|
|$x_{0}$                      | $2.706$| $3.841$| $6.635$| $7.879$ | $10.828$|

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