
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
Observe the following expressions:
$$(x - 1)(x + 1) = x^2 - 1$$
$$(x - 1)(x^2 + x + 1) = x^3 - 1$$
$$(x - 1)(x^3 + x^2 + x + 1) = x^4 - 1,$$
Based on the pattern of the preceding expressions, the general form of $(x - 1)(x^n + x^{n-1} + ... + x + 1)=$ __________ (where $n$ is a positive integer).

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