
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 propositions: $p$: For any $a\in[1, 2]$, the inequality $|\text{m}-5|\leqslant\sqrt{a^{2}+8}$ always holds; $q$: The function $f(x)=x^{3}+mx^{2}+(m+6)x+1$ has a maximum value and a minimum value. Find the range of values of $m$ that makes the proposition "$p$ and $\neg q$" true.

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