
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 $f(x)= \frac{1}{2}ax^2-(2a+1)x+2\ln x$ (where $x \in \mathbb{R}$),
(I) If the tangents to the curve $y=f(x)$ at $x=1$ and $x=3$ are parallel, find the value of $a$.
(II) Determine the intervals of increase and decrease for $f(x)$.

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