
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 a certain region, Chinese, Mathematics, and English are compulsory subjects for candidates in the new college entrance examination. Candidates also need to choose three subjects from Physics, Chemistry, Biology, History, Geography, and Politics as elective subjects. $200$ students who have already selected subjects in this region are randomly selected for a statistical analysis. It is found that $60\%$ chose Physics, $75\%$ chose Politics, and $80$ students chose both Physics and Politics.

$(1)$ Complete a $2\times 2$ contingency table for the number of students who chose Physics and Politics, and determine whether it can be considered that the selection of Physics is related to the selection of Politics, with the premise that the probability of making an error does not exceed $0.1\%$.

$(2)$ If three students, A, B, and C, choose Physics, Chemistry, and Biology, and students A and B choose History, Geography, and Politics, two students are randomly selected from these five students. Find the probability that one student chose Physics and the other chose Politics.

Given reference data and formula:

$P(K^{2}\geqslant k_{0})$

|$0.15$|$0.10$|$0.05$|$0.025$|$0.010$|$0.005$|$0.001$|
|---|---|---|---|---|---|---|---|
|$k_{0}$|$2.072$|$2.706$|$3.841$|$5.024$|$6.635$|$7.879$|$10.828$|

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

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