
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
Let the function $f(x)=\ln x+x^{2}-ax$ where $a \in \mathbb{R}$.

(I) When $a=3$, determine the intervals of monotonicity for the function $f(x)$.

(II) If the function $f(x)$ has two extreme points $x_{1}$ and $x_{2}$, and $x_{1} \in (0,1]$, find the minimum value of $f(x_{1})-f(x_{2})$.

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