
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 $\left(x-1\right)\left(x+1\right)=x^{2}-1$, $\left(x-1\right)(x^{2}+x+1)=x^{3}-1$, $\left(x-1\right)(x^{3}+x^{2}+x+1)=x^{4}-1$. According to the patterns in the previous equations, we can obtain: the unit digit of $2^{2023}+2^{2022}+2^{2021}+2^{2020}+\ldots +2^{2}+2+1$ is ______.

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