
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 functions $f(x) = \ln(x+1) - ax$ and $g(x) = ax^2$ where $a \in \mathbb{R}$.
(I) Discuss the monotonic intervals of the function $f(x)$;
(II) Let $h(x) = f(x) + g(x)$, discuss the number of extremum points of the function $h(x)$ and explain the reasons.

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