
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 $a \in \mathbb{R}$, let $f(x) = \ln x - ax$.
(I) Find the interval(s) where $f(x)$ is strictly increasing.
(II) Let $F(x) = f(x) + ax^2 + ax$. Determine if $F(x)$ has any extreme values (maximum or minimum). If they exist, find them and provide a reason.

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