
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 $f(x)=\ln x-mx (m\in R)$.
(I) Discuss the monotonic intervals of the function $f(x)$;
(II) When $m\geqslant \frac{ 3 \sqrt {2}}{2}$, let $g(x)=2f(x)+x^{2}$ and its two extreme points $x\_1$, $x\_2 (x\_1 < x\_2)$ are exactly the zeros of $h(x)=\ln x-cx^{2}-bx$. Find the minimum value of $y=(x\_1-x\_2)h′( \frac {x\_1+x\_2}{2})$.

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