
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
Determine the formula that relates $x$ to $y$ in the following table:
\[\begin{tabular}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5\\ \hline y & -1 & 3 & 9 & 17 & 27\\ \hline\end{tabular}\]
A) $y = x^2 + x - 3$
B) $y = x^2 - x + 1$
C) $y = x^2 - 2x - 3$
D) $y = 2x^2 + x - 1$
E) $y = x^2 + 2x - 1$

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