
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 $f(x)=2x^{3}-3(a+1)x^{2}+6ax$, where $a\in \mathbb{R}$,

(1) The slope of the tangent line to the curve $y=f(x)$ at $x=0$ is $3$, find the value of $a$;

(2) If for any $x\in(0,+\infty)$, $f(x)+f(-x)\geqslant 12\ln x$ always holds, find the range of values for $a$;

(3) If $a > 1$, let the maximum and minimum values of the function $f(x)$ on the interval $[1,2]$ be $M(a)$ and $m(a)$ respectively, and let $h(a)=M(a)-m(a)$, find the minimum value of $h(a)$.

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