
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
Let the quadratic function $f(x)=ax^{2}+bx+c\ (a\neq 0)$ have a derivative denoted by $f'(x)$, and $f'(0) > 0$. If for all $x\in\mathbb{R}$, it always holds that $f(x)\geqslant 0$, then the minimum value of $\dfrac{f(1)}{f'(0)}$ is \_\_\_\_\_.

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