
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
Evaluate the expression:
\[
\left(\frac{x^4+1}{x}\right)\left(\frac{y^4+1}{y}\right)+\left(\frac{x^4-1}{y}\right)\left(\frac{y^4-1}{x}\right)
\]
where $xy \neq 0$.
A) $2x^3y^3 + \frac{2}{xy}$  
B) $2x^2y^2 + 2$  
C) $2xy + \frac{2}{xy}$  
D) $\frac{2x^2}{y^2} + \frac{2y^2}{x^2}$  
E) $x^3y^3 + xy$

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