
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 total of 1000 students from a certain school participated in the "Belt and Road" knowledge competition, with 400 boys. In order to understand the performance of the students in the knowledge competition, a stratified random sampling method was used to select 100 students for a survey. The scores ranged from 450 to 950 points, and students with scores of 750 points or higher were called "high-scoring players." It is known that there are 25 "high-scoring players" in the sample, including 10 girls.<br/>$(1)$ Complete the table below;<br/><table><tbody><tr><td width="76"></td><td width="200">Belong to "high-scoring players"</td><td width="201">Do not belong to "high-scoring players"</td><td width="76">Total</td></tr><tr><td>Boys</td><td></td><td></td><td></td></tr><tr><td>Girls</td><td></td><td></td><td></td></tr><tr><td>Total</td><td></td><td></td><td></td></tr></tbody></table>$(2)$ Determine whether there is a 97.5% confidence that the students in this school are related to "high-scoring players" and "gender"?<br/>Reference formula: ${K}^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.<br/><table><tbody><tr><td>$P(K^{2}\geqslant k_{0})$</td><td>$0.150$</td><td>$0.100$</td><td>$0.050$</td><td>$0.025$</td><td>$0.010$</td><td>$0.005$</td><td>$0.001$</td></tr><tr><td>$k_{0}$</td><td>$2.072$</td><td>$2.706$</td><td>$3.841$</td><td>$5.024$</td><td>$6.635$</td><td>$7.879$</td><td>$10.828$</td></tr></tbody></table>

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