Determine all pairs $(a, b)$ of real numbers for which there exists a unique symmetric $2 \times 2$ matrix $M$ with real entries satisfying $\operatorname{trace}(M)=a$ and $\operatorname{det}(M)=b$. Please provide the value of $a + b$ for the unique pair $(a, b)$.

Let's think step by step and output the final answer within \boxed{}.
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