
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 that $max{a,b}= \begin{cases} a,a\geqslant b \\ b,a < b\end{cases}$, and $M=max{|x-y^{2}+4|,|2y^{2}-x+8|}$, if $M\geqslant m^{2}-2m$ holds true for all real numbers $x$ and $y$, then the range of values for the real number $m$ is _______.

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