
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 equations:
$$(a-b)(a+b)=a^2-b^2$$
$$(a-b)(a^2+ab+b^2)=a^3-b^3$$
$$(a-b)(a^3+a^2b+ab^2+b^3)=a^4-b^4$$
$$(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)=a^5-b^5$$
From these, we can conjecture that for $a^n-b^n=$ (where $n \in \mathbb{N}_+$ and $N \geq 2$).

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