
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 was conducted on the products produced by these two production lines. A random sample of 300 items was taken from the products produced by these two production lines for evaluation, and 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 the product quality is related to the production line?<br/>$(2)$ Further analysis was conducted on the products. From the products evaluated as "fair," a stratified random sample of 6 items was taken based on the production line. If 2 items are randomly selected from these 6 items, find the probability that at least one of the 2 items is produced by Line A.<br/>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}
user