
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 proposition $p$: The equation $x^{2}-2ax+2a^{2}-a-6=0$ has real roots for $x$, proposition $q: m-1\leq a\leq m+3$.  
$(Ⅰ)$ If proposition $\neg p$ is true, find the range of real number $a$;  
$(Ⅱ)$ If $p$ is a necessary but not sufficient condition for $q$, find the range of real number $m$.

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