
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 plots the graph of the function \( y = ax^2 + bx + c \) (\( a \neq 0 \)) by taking 7 values of the independent variable \( x_1 < x_2 < \cdots < x_7 \) such that \( x_2 - x_1 = x_3 - x_2 = \cdots = x_7 - x_6 \), and calculates the corresponding values of \( y \). The results are listed in the table below.
\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}

Due to a calculation mistake, one of the \( y \) values is incorrect. Identify the incorrect value and provide the correct value, along with an explanation.

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