
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 $f(x) = \frac{1}{2}x^2 - x + \ln x$.

(I) Find the range of the slope angles of the tangents at all points on the graph of the function $f(x)$.

(II) If $F(x) = f(x) - ax$, where $a \in \mathbb{R}$, discuss the monotonicity of $F(x)$.

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