
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 $f(x)=ax^{2}+bx-\ln x$ $(a,b\in\mathbb{R})$

(I) Assume $a\geqslant 0$, find the intervals of monotonicity for $f(x)$.

(II) Assume $a > 0$, and for any $x > 0$, $f(x)\geqslant f(1)$. Compare the magnitude of $\ln a$ and $-2b$.

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