
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 $f(x)=-x^2+ax$ ($a \in \mathbb{R}$), 
(1) when $a=3$, find the maximum and minimum value of the function $f(x)$ on the interval $\left[\frac{1}{2}, 2\right]$;
(2) when the function $f(x)$ is monotonic on the interval $\left(\frac{1}{2}, 2\right)$, find the range of values for $a$.

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