
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 $p$: $\forall x \in [1,2]$, $x^{2}-a\geqslant 0$; and $q$: $\exists x_{0} \in R$, such that $x_{ 0 }^{ 2 }+(a-1)x_{0}+1 < 0$. If "$p$ or $q$" is true and "$p$ and $q$" is false, then the range of the real number $a$ is \_\_\_\_\_\_.

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