
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 $f(x)=-x^{2}+ax-\ln x$ $(a\in\mathbb{R})$.
- $(I)$ When $a=3$, find the maximum and minimum values of the function $f(x)$ on the interval $\left[\frac{1}{2},2\right]$.
- $(II)$ If the function $f(x)$ has both a maximum and a minimum value, find the range of the real number $a$.

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