
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
The polynomial \( h(x) = x^3 - x^2 - 4x + 4 \) has three distinct roots. Let \( p(x) = x^3 + ax^2 + bx + c \) be a cubic polynomial with leading coefficient 1 such that the roots of \( p(x) \) are the cubes of the roots of \( h(x) \). Find the ordered triple \( (a, b, c) \).

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