
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 $p$: For $m \in [-1,1]$, the inequality $a^{2}-5a-3 \geqslant \sqrt{m^{2}+8}$ always holds; proposition $q$: The inequality $x^{2}+ax+2 < 0$ has a solution. If $p$ is true and $q$ is false, find the range of values for $a$.

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