
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
Initially, the polynomials $x^{3}-3x^{2}+5$ and $x^{2}-4x$ are written on the board. If the polynomials $f(x)$ and $g(x)$ are already written on the board, it is allowed to write the polynomials $f(x) \pm g(x), f(x) g(x), f(g(x))$ and $c f(x)$, where $c$ is an arbitrary (not necessarily integer) constant. Can a polynomial of the form $x^{n}-1$ (for natural $n$) appear on the board after several operations?

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