
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 $a\in\mathbb{R}$. If for any $a\in[-3,0]$ and any $x_1, x_2\in[0,2]$, the inequality $m-am^2\geqslant |f(x_1)-f(x_2)|$ always holds, find the range of values for the real number $m$.

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