
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
A math interest group found:<br/>$(x-1)\left(x+1\right)=x^{2}-1$;<br/>$(x-1)(x^{2}+x+1)=x^{3}-1$;<br/>$(x-1)(x^{3}+x^{2}+x+1)=x^{4}-1$;<br/>By using the discovered pattern, find: $6^{2023}+6^{2022}+6^{2021}+\ldots +6+1=\_\_\_\_\_\_$.

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