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

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