
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
(1) Given the function $\Delta =36-36a=36(1-a)$, and the function $f(x)=a\ln (x+1)-x^{2}$, for any two real numbers $p,q$ taken from the interval $(0,2)$, and $p\ne q$, if the inequality $\dfrac{f\left( p+1 \right)-f\left( q+1 \right)}{p-q} > 1$ always holds, then the range of values for the real number $a$ is ______.

(2) Let the function $f(x)=(x-a)(x-b)(x-c)$, where $a$, $b$, $c$ are distinct constants, then $\dfrac{a}{f'(a)}+ \dfrac{b}{f'(b)}+ \dfrac{c}{f'(c)} =$ ______.

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