
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
Factorize the following expression without grouping the terms:

$$
x^{8}-x^{7} y+x^{6} y^{2}-x^{5} y^{3}+x^{4} y^{4}-x^{3} y^{5}+x^{2} y^{6}-x y^{7}+y^{8}
$$

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