
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 observations $(x_i, y_i)$, after plotting the scatter diagram, it is determined that there is a linear correlation. If for $\overline{y}= \overline{b}x+ \overline{a}$, it is found that $\overline{b} =0.51$, $\overline{x}=61.75$, $\overline{y}=38.14$, calculate the regression equation.

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