
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
Create a new polynomial \( f(x) = x^3 - 2x^2 + 3x - 1 \) and determine a polynomial \( g(x) \) such that the roots of \( g(x) \) are the cubes of the roots of \( f(x) \). Find the ordered triple \( (b, c, d) \) for \( g(x) = x^3 + bx^2 + cx + d \) with leading coefficient 1.

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