
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) When $a=8$, $b=-6$, find the number of zeros of $f(x)$.  
(II) Suppose $a>0$, and $x=1$ is a local minimum point of $f(x)$, compare the size of $\ln a$ and $-2b$.

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