
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 $p$: $x^{2}-8x-20\leqslant 0$; $x^{2}+2x+1-m4\leqslant 0$.

$(1)$ If $p$ is a necessary condition for $q$, find the range of values for $m$;

$(2)$ If $\neg p$ is a necessary condition for $\neg q$, find the range of values for $m$;

$(3)$ If $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of values for $m$.

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