
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 high school's second-year students are studying the relationship between students' math and Chinese scores. They conducted a simple random sampling with replacement and obtained a sample of size $200$ from the second-year students. The sample observation data of math scores and Chinese scores are organized as follows:

|          | Chinese Score |         |         | Total |
|----------|---------------|---------|---------|-------|
| Math Score | Excellent     | Not Excellent |         |       |
| Excellent | $45$          | $35$    |         | $80$  |
| Not Excellent | $45$          | $75$    |         | $120$ |
| Total    | $90$          | $110$   |         | $200$ |

$(1)$ According to the independence test with $\alpha = 0.01$, can it be concluded that there is an association between math scores and Chinese scores?  
$(2)$ In artificial intelligence, $L(B|A)=\frac{{P(B|A)}}{{P(\overline{B}|A)}}$ is commonly used to represent the odds of event $B$ occurring given that event $A$ has occurred, which is called likelihood ratio in statistics. Now, randomly select a student from the school, let $A=$"the selected student has a non-excellent Chinese score" and $B=$"the selected student has a non-excellent math score". Please estimate the value of $L(B|A)$ using the sample data.  
Given: ${\chi^2}=\frac{{n{{(ad-bc)}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$  
| $\alpha $ | $0.05$ | $0.01$ | $0.001$ |
|-----------|--------|--------|---------|
| $x_{a}$   | $3.841$| $6.635$| $10.828$|

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