
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 $f(x)=\ln x$.
(1) The equation $f(x+a)=x$ has exactly one real solution. Find the value of $a$.
(2) If the function $g(x)=f(x)+ \frac{1}{2}x^{2}-mx (m\geqslant \frac{5}{2})$ has extreme points $x\_1$, $x\_2 (x\_1 < x\_2)$ that 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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