
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 $y$, where $(1,y_1)$, $(5,y_2)$, $(7,y_3)$, $(13,y_4)$, $(19,y_5)$, and given the linear regression equation $\hat{y} = 2x + 45$, determine the value of $\overline{y}$.

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