
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
(1) Given $2 < x < 3$ and $-2 < y < -1$, find the range of values for $x+y$, $x-y$, and $xy$;  
(2) Let $x < y < 0$, compare the size of $(x^2+y^2)(x-y)$ and $(x^2-y^2)(x+y)$.

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