
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
(Full score for this sub-question is 13 points)

Given the function $f(x) = -x^2 + ax - \ln(x)$ $(a \in R)$.

(1) Find the necessary and sufficient condition for the function $f(x)$ to have both a maximum and a minimum value.

(2) When the function $f(x)$ is monotonic on the interval $[1, 2]$, find the range of values for $a$.

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