
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 $f(x)=\ln (x+a), a\in R$.
(I) Find the value of $a$ such that the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is parallel to the line $x-2y+1=0$;
(II) When $a=0$, if the extreme points $x\_1$, $x\_2 (x\_1 < x\_2)$ of the function $g(x)=f(x)+ \frac {1}{2}x^{2}-mx (m\geqslant \frac {5}{2})$ are exactly the zeros of the function $h(x)=f(x)-cx^{2}-bx$, 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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