
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 the relationship between $x$ and $y$ as detailed in the table:
\[\begin{tabular}[t]{|c|c|c|c|c|c|}\hline x&0&1&2&3&4\\\hline y&200&150&80&0&-140\\\hline\end{tabular}\]
What is the formula that expresses this relationship?
**A)** $y = -10x^3 + 20x^2 - 60x + 200$
**B)** $y = 10x^3 - 20x^2 + 60x - 200$
**C)** $y = -5x^3 + 15x^2 - 40x + 200$
**D)** $y = 20x^3 - 10x^2 + 30x - 100$
**E)** $\text{None of these}$

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