
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 following facts:
$(a-b)(a+b)=a^{2}-b^{2}$,
$(a-b)(a^{2}+ab+b^{2})=a^{3}-b^{3}$,
$(a-b)(a^{3}+a^{2}b+ab^{2}+b^{3})=a^{4}-b^{4}$,
$(a-b)(a^{4}+a^{3}b+a^{2}b^{2}+ab^{3}+b^{4})=a^{5}-b^{5}$,
what is a reasonable conjecture?

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