
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

Decompose the expression

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

into a product of three rational integer expressions with respect to $x$ and $y$.

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