
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
Simplify the fraction $\frac{x^{8}+x^{6} y^{2}+x^{4} y^{4}+x^{2} y^{6}+y^{8}}{x^{4}+x^{3} y+x^{2} y^{2}+x y^{3}+y^{4}}$ and calculate its value for $x=0.01$ and $y=0.02$.

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