
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 factory focuses on technological innovation in production processes and has designed and tested two production lines, A and B. An evaluation of the products produced on these two production lines was conducted by randomly selecting 300 items for assessment. The evaluation results ("good" or "fair") were compiled into a contingency table as shown below:

|          | Fair | Good | Total |
|----------|------|------|-------|
| Line A   | 40   | 80   | 120   |
| Line B   | 80   | 100  | 180   |
| Total    | 120  | 180  | 300   |

$(1)$ By calculation, can we be $90\%$ confident that product quality is related to the production line?<br/>$(2)$ Further analysis of the products: from the items rated as "fair," 6 items were sampled using stratified sampling by production line. If 2 items are randomly selected from these 6 items, what is the probability that at least one of the 2 items is from production line A?

Given table and formula:<br/>

| $P(K^{2}\geqslant k_{0})$ | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 |
|---------------------------|------|------|------|-------|-------|
| $k_{0}$                   | 2.072| 2.706| 3.841| 5.024 | 6.635 |

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

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