
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
Jessica finds a torn piece of paper with the top part of a monic polynomial of degree \( n \) visible. The terms that can be seen are \( x^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + a_{n-3}x^{n-3} \), and it is noted that \( a_{n-1} = -a_{n-2} \). Jessica discerns from the scribbles that her challenge is to find the sum of the cubes of the roots of this polynomial. She is aware that \( a_{n-1} = -2 \) and \( a_{n-3} = 0 \). Determine the sum of the cubes of the roots.

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