
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
Consider the function $f(x) = \ln x + \frac{1}{2}x^2 + ax$ where $a \in \mathbb{R}$, and another function $g(x) = e^x + \frac{3}{2}x^2$.
(1) Discuss the number of extreme points of $f(x)$.
(2) If for all $x > 0$, $f(x) \le g(x)$ always holds, find the range of the real number $a$.

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