
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
A certain school conducted a survey on students' exercise habits by stratified sampling $100$ students based on gender. The survey results are summarized in the table below:

|         | Likes | Dislikes | Total |
|---------|-------|----------|-------|
| Boys    |       | $10$     |       |
| Girls   | $20$  |          |       |
| Total   |       |          | $100$ |

It is known that when randomly selecting $1$ person from all $100$ individuals, the probability of selecting someone who dislikes exercising is $0.4$.

$(1)$ Please complete the above contingency table.

$(2)$ Is there a $99.9\%$ certainty that liking exercise is related to gender? Explain your reasoning. (Reference data is shown in the table below, results are rounded to $3$ decimal places)

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

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

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