
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 $p$ and $q$:
- Proposition $p$: The function $f(x)=x^{2}+ax-2$ has exactly one root in the interval $[-1,1]$.
- Proposition $q$: The inequality $x^{2}+3(a+1)x+2 \leqslant 0$ holds true for all $x$ in the interval $[\frac{1}{2}, \frac{3}{2}]$.
If the compound proposition "$p$ and $q$" is false, find the range of values for the real number $a$.

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