
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 $f(x)=c\ln x+ \frac {1}{2}x^{2}+bx(b,c∈R,c​≠ 0)$, where $x=1$ is the extreme point of $f(x)$:
(I) Find the analytical expression of the function $f(x)$ if the tangent line at $x=2$ is parallel to $3x-4y+4=0$;
(II) Find the range of the real number $c$ if $f(x)=0$ has exactly two solutions.

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