
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 chemical plant needs to study the correlation between the recovery rate of a product $y$ and the content of effective components in the raw material $x$ to predict the recovery rate of the product. Now, 8 pairs of observation values are taken, and it is calculated that $\sum\limits_{i=1}^{8}x_{i}=52$, $\sum\limits_{i=1}^{8}y_{i}=228$, $\sum\limits_{i=1}^{8} x_{ i }^{ 2 }=478$, $\sum\limits_{i=1}^{8}x_{i}y_{i}=1\,849$. The regression line equation between $y$ and $x$ is \_\_\_\_\_\_. (Round to 0.01)

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