
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
Consider that a portion of the graph of the polynomial $g(x) = Ax^3 + Bx^2 + Cx + D$ is observed, and it includes specific points implying the function passes through $(3, y)$, where $y = g(3) = 1$. Assume points on the graph indicate $A = -1, B = 1, C = -1, D = 1$. Determine the value of $12A - 6B + 3C - D$.

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