
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 $p: -2 \leq x \leq 11$, $q: 1 - 3m \leq x \leq 3 + m$ ($m > 0$), if $\neg p$ is a necessary but not sufficient condition for $\neg q$, then the range of values for the real number $m$ is ____. If the proposition "$x^2 - 2x + m \leq 0$" is a false statement, then the range of values for the real number $m$ is ____.

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