
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 $f(x)=c\ln x+\frac{1}{2}x^2+bx$ ($b,c\in\mathbb{R}, c\neq 0$), where $x=1$ is the extreme point of $f(x)$.

(I) If $x=1$ is the maximum point of $f(x)$, find the monotonic interval of $f(x)$ (represented by $c$);

(II) If $f(x)=0$ has exactly two solutions, find the range of values for the real number $c$.

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