
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
Given $x>0$, $y>0$, and the sets $A=\{x^2+2, -x, -x-1\}$, $B=\{-y, -\frac{y}{2}, y+1\}$:  
(1) If $A=B$, find the value of $x^2+y^2$;  
(2) If $A\cap B=\{6\}$, find $A\cup B$.

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