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

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