
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 randomly surveyed $100$ students and found that $60$ of them like outdoor sports. They then conducted a physical test on them and obtained the following incomplete $2\times 2$ contingency table:

| Category | Likes Outdoor Sports | Does Not Like Outdoor Sports | Total |
|----------|----------------------|------------------------------|-------|
| Non-Excellent Test Score | $10$ | $15$ |       |
| Excellent Test Score |       |       | $75$  |
| Total |       |       | $100$ |

$(1)$ Complete the $2\times 2$ contingency table.  
$(2)$ Based on the contingency table analysis, can we be $95\%$ confident that the students' performance in the physical test at this school is related to their preference for outdoor sports?  
Given: ${K^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$, where $n=a+b+c+d$.  
$K^2$ values and corresponding probabilities are given in the table below:

| $k_{0}$ | $2.706$ | $3.841$ | $6.635$ | $7.879$ | $10.828$ |
|---------|---------|---------|---------|---------|----------|
| $P(K^{2}\geqslant k_{0})$ | $0.10$ | $0.05$ | $0.01$ | $0.005$ | $0.001$ |

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