
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 that points $(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4)$ are plotted, where $x_1 < x_2 < x_3 < x_4$, $x_4 - x_3 = x_3 - x_2 = d$, and $x_2 - x_1 = 2d$, and $y_1 + y_4 = y_2 + y_3$, determine the slope of the line which best fits the data.

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