
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 the propositions $p$: $\forall x \in \mathbb{R}$, $x^{2}-2x > a$; and $q$: $\exists x_{0} \in \mathbb{R}, x_{0}^{2}+2ax_{0}+2-a=0$. If the proposition "$p \vee q$" is true and "$p \wedge q$" 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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