
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 $f(x) = \frac{1}{3}x^3 + ax^2 + bx$ (where $a, b \in \mathbb{R}$),
(I) Find the intervals of monotonicity for $f(x)$ when $a=1$;
(II) If $f(1) = \frac{1}{3}$, and $f(x)$ has no extreme points in the interval $(0, \frac{1}{2})$, find the range of values for $a$.

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