
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
If $\left(x+y\right)\left(x+y-2\right)-3=0$, let $P=x+y$, the original expression can be transformed into $\left(x+y\right)^{2}-2\left(x+y\right)-3=0$, that is $P^{2}-2P-3=0$. Solving this equation gives $P_{1}=3$ and $P_{2}=-1$. Therefore, the value of $x+y$ is $3$ or $-1$. Following the same method, calculate the value of $a^{2}+b^{2}$ when $(a^{2}+b^{2})(a^{2}+b^{2}-4)-5=0$ is ______.

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