
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 Sichuan, the new college entrance examination was launched in 2022, and the first new college entrance examination will be implemented in 2025. The new college entrance examination adopts the "$3+1+2$" mode. "$3$" refers to the three national unified examination subjects of Chinese, Mathematics, and Foreign Languages, regardless of whether they are arts or sciences; "$1$" refers to choosing one subject from Physics and History; "$2$" refers to choosing two subjects from Political Science, Geography, Chemistry, and Biology. The subject selection situation of the first-year high school students in a certain school in 2022 is shown in the table below:

| Subject Combination | Physics, Chemistry, Biology | Physics, Chemistry, Political Science | Physics, Chemistry, Geography | History, Political Science, Geography | History, Political Science, Biology | History, Chemistry, Political Science | Total |
|---------------------|-----------------------------|-------------------------------------|-----------------------------|--------------------------------------|----------------------------------|--------------------------------------|-------|
| Male                | 180                         | 80                                  | 40                          | 90                                   | 30                               | 20                                   | 440   |
| Female              | 150                         | 70                                  | 60                          | 120                                  | 40                               | 20                                   | 460   |
| Total               | 330                         | 150                                 | 100                         | 210                                  | 70                               | 40                                   | 900   |

$(1)$ Complete the $2\times 2$ contingency table below and determine if there is a $99\%$ certainty that "choosing Physics is related to the gender of the student":

|                   | Choose Physics | Do not choose Physics | Total |
|-------------------|----------------|-----------------------|-------|
| Male              |                |                       |       |
| Female            |                |                       |       |
| Total             |                |                       |       |

$(2)$ From the female students who chose the combinations of History, Political Science, Biology and History, Chemistry, Political Science, select 6 students using stratified sampling to participate in a history knowledge competition. Find the probability that the 2 selected female students are from the same combination.

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

| $P(K^{2}\geqslant k_{0})$ | 0.15 | 0.1  | 0.05 | 0.01 |
|---------------------------|------|------|------|------|
| $k_{0}$                   | 2.072| 2.706| 3.841| 6.635|

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