
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 $f(x)=c\ln x+ \frac{1}{2}x^{2}+bx (b,c\in R, c\neq 0)$, and $x=1$ 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 the real number $c$.

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