
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
Consider the scenario where you plot income \(y\) against years of experience \(x\) for three individuals to obtain the points \((x_1, y_1), (x_2, y_2), (x_3, y_3)\) where \(x_1 < x_2 < x_3\) and \(x_3 = 2x_2 - x_1 + 5\). Calculate the slope of the regression line, the line that minimizes the sum of squared deviations of \(y\) from the predicted values.
A) \( \frac{y_3-y_1}{x_3-x_1} \)
B) \( \frac{(y_2-y_1)-(y_3-y_2)}{x_3-x_1} \)
C) \( \frac{2y_3-y_1-y_2}{2x_3-x_1-x_2} \)
D) \( \frac{y_2-y_1}{x_2-x_1}+\frac{y_3-y_2}{x_3-x_2} \)
E) None of these

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