
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 (x<sub>1</sub>, y<sub>1</sub>), (x<sub>2</sub>, y<sub>2</sub>), … (x<sub>n</sub>, y<sub>n</sub>) with a linear relationship between two variables, the regression line equation is $\hat y = bx + 0.2$. If the mean of x<sub>1</sub>, x<sub>2</sub>, …, x<sub>n</sub> is $\overline{x} = 4$, and the mean of y<sub>1</sub>, y<sub>2</sub>, …, y<sub>n</sub> is $\overline{y} = 5$, find the approximate value of y when x=2.

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