
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
Please carefully read the following information before answering the question:

Given $\left(x+y-3\right)\left(x+y+4\right)=-10$, find the value of $x+y$.

Let $t=x+y$, then the original equation transforms into $\left(t-3\right)\left(t+4\right)=-10$, which simplifies to $t^{2}+t-2=0$.

Therefore, $\left(t+2\right)\left(t-1\right)=0$ gives $t_{1}=-2$ and $t_{2}=1$. Hence, $x+y=-2$ or $x+y=1$.

Answer the question: (1) Given $\left(x^{2}+y^{2}-4\right)\left(x^{2}+y^{2}+2\right)=7$, find the value of $x^{2}+y^{2}$.

(2) Solve the equation: $x^{4}-6x^{2}+8=0$.

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