
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
A student plotted the graph of the function \( y = ax^2 + bx + c \) (\(a \neq 0\)) by choosing 7 different values for the variable \( x \): \( x_1 < x_2 < \cdots < x_7 \). They set \( x_2 - x_1 = x_3 - x_2 = \cdots = x_7 - x_6 \) and calculated the corresponding \( y \) values, creating the following table:
\[
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$x$ & $x_1$ & $x_2$ & $x_3$ & $x_4$ & $x_5$ & $x_6$ & $x_7$ \\
\hline
$y$ & 51 & 107 & 185 & 285 & 407 & 549 & 717 \\
\hline
\end{tabular}
\]

However, due to a calculation error, one of the \( y \) values is incorrect. Which \( y \) value is incorrect, what should the correct value be, and why?

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