
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 \\(a{x}^{2}+2x+b \geqslant 0 \\) holds for all real numbers, and there exists \\(x_{0} \in \mathbb{R}\\), such that \\(ax_{0}^{2}+2{x_{0}}+b=0\\), then the minimum value of \\(\dfrac{a^{2}+b^{2}}{a-b}\\) is \_\_\_\_\_\_\_\_\_.

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