
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 pattern of the expressions $\left(x-1\right)\left(x^{n}+x^{n-1}+x^{n-2}+\cdots+x+1\right) = x^{n+1} - 1$, find the value of $x^{2021}-1$ when $\left(x-1\right)(x^{5}+x^{4}+x^{3}+x^{2}+x+1)=0$.

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