
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 $f(x)=\frac{1}{2}x^{2}+mx+6\ln x (m∈R)$.

(I) If the tangent line of the curve $y=f(x)$ at the point $(1,f(1))$ is parallel to the line $y=2x-1$, find the analytical expression of the function $f(x)$;

(II) Let $g(x)=f(x)-x^{2}+x$, if the function $g(x)$ is monotonically increasing on $(0,1]$, find the range of $m$.

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