
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

...

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system
A certain school in a province uses the new college entrance examination mode. Students participate in the college entrance examination by selecting subjects in the "$3+1+2$" mode: "$3$" refers to the three compulsory subjects of Chinese, Mathematics, and Foreign Language in the national unified college entrance examination; "$1$" is the subject chosen by the candidates from Physics and History; "$2$" is the two subjects chosen by the candidates from Ideological and Political Education, Geography, Chemistry, and Biology.  
$(Ⅰ)$ To understand the subject selection preferences of the students in this school, a random sample of 100 students was surveyed from the 750 students of this year, and the following partial data distribution was obtained:  

|         | Physics | History | Total |
|---------|---------|---------|-------|
| Boys    | 30      |         | 40    |
| Girls   |         |         |       |
| Total   | 50      |         | 100   |

Please fill in the remaining 5 blanks in the table above and determine whether there is a 99.9% certainty that the "subject selection direction of students" is related to the "gender of students";  
$(Ⅱ)$ Two students, A and B, who have chosen the Physics direction, in the "4 choose 2" subject selection, find the probability that they choose exactly one subject in common.  
Given: ${K^2}=\frac{{n{{(ad-bc)}^2}}}{{(a+b)(c+d)(a+c)(b+d)}},n=a+b+c+d$.  

| $P(K^{2}\geqslant k_{0})$ | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
|---------------------------|------|------|-------|-------|-------|-------|
| $k_{0}$                   | 2.706| 3.841| 5.024 | 6.635 | 7.879 | 10.828|

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