
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 $p: \exists x \in \mathbb{R}$, $x^{2} + ax + 2 = 0$ and $q: \forall 0 < x < 1$, $x^{2} - a < 0$.  
$(1)$ If $p$ is a true proposition, find the range of values for $a$.  
$(2)$ If one of $p$ or $q$ is true and the other is false, find the range of values for $a$.

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