
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 polynomial $h(x) = x^3 - 2x^2 + 3x - 4$, which has three distinct roots, find a cubic polynomial $j(x) = x^3 + ax^2 + bx + c$ such that the roots of $j(x)$ are the cubes of the roots of $h(x)$. Determine the ordered triple $(a, b, c)$.

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