
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 relationship between the recovery rate of a product ($y$) and the content of effective components in the raw material. After taking $8$ pairs of observations, the following sums were calculated: $\sum\limits^{8}_{i=1}x_i=52$, $\sum\limits^{8}_{i=1}y_i=228$, $\sum\limits^{8}_{i=1}x_i^2=478$, $\sum\limits^{8}_{i=1}x_iy_i=1,849$. Find the linear regression equation between $y$ and $x$.

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