
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 $f(x)=ax^{2}+bx-2\ln x$ ($a > 0$, $b\in\mathbb{R}$), if for any $x > 0$, $f(x)\geqslant f(2)$ holds, find the inequality involving $a$ and $b$.

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