
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 $f(x) = \ln x + \frac{1}{2}ax^2 + bx, a, b \in \mathbb{R}$.

(I) If $a = -2, b = 1$, find the monotonic intervals of the function $f(x)$.

(II) If for any $a \in [1, +\infty)$, $f(x) \geqslant 0$ holds true for $x \in [1, +\infty)$, find the range of values for the real number $b$.

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