
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) If the equation $f(x+a)=x$ has exactly one real solution, find the value of $a$.

(2) If the extreme points $x\_1$, $x\_2 (x\_1 < x\_2)$ of the function $g(x)=f(x)+ \frac{1}{2}x^{2}-mx \left( m\geqslant \frac{5}{2} \right)$ are exactly the zeros of the function $h(x)=f(x)-cx^{2}-bx$, find the minimum value of $y=(x\_1-x\_2)h'\left( \frac{x\_1+x\_2}{2} \right)$.

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