
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
Factor the following expression:
\[
\frac{(x^3 - y^3)^3 + (y^3 - z^3)^3 + (z^3 - x^3)^3}{(x - y)^3 + (y - z)^3 + (z - x)^3}.
\]

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