
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 the function $f(x)=ax^{2}+bx+c$ where $(0 < 2a < b)$, it always holds that $f(x) \geqslant 0$ for any $x \in \mathbb{R}$. The minimum value of the expression $\dfrac {f(1)}{f(0)-f(-1)}$ is \_\_\_\_\_\_.

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