
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 that $a$ is a real number, $p$: The point $M(1,1)$ is inside the circle $(x+a)^{2}+(y-a)^{2}=4$; $q$: $\forall x \in R$, $x^{2}+ax+1 \geqslant 0$.
(1) If $p$ is a true proposition, find the range of values for $a$;
(2) If $q$ is a false proposition, find the range of values for $a$;
(3) If "$p$ and $q$" is a false proposition, and "$p$ or $q$" is a true proposition, find the range of values for $a$.

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