
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
Given a set of data corresponding to the variables $x$ and $y$, $(3,y_{1})$, $(5,y_{2})$, $(7,y_{3})$, $(12,y_{4})$, $(13,y_{5})$, a linear regression equation $\hat{y}=\frac{1}{2}x+20$ is obtained. Find the value of $\overline{y}$.

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