
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
Let max{a, b} be defined as $$\begin{cases} a, & \text{if } a \geq b \\ b, & \text{if } a < b \end{cases}$$, and let $M = \max\{|x-y^2+4|, |2y^2-x+8|\}$. If for all real numbers $x, y$, it holds that $M \geq m^2 - 2m$, then the range of values for the real number $m$ is \_\_\_\_\_\_.

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