
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 $a > b$, the quadratic trinomial $ax^{2}+2x+b\geqslant 0$ holds for all real numbers $x$, and there exists $x_{0}\in\mathbb{R}$ such that $ax_{0}^{2}+2x_{0}+b=0$ holds, find the minimum value of $\dfrac {a^{2}+b^{2}}{a-b}$.

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