
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 proposition $p$: $∀x∈[1,12]$, $x^{2}-a≥0$. Proposition $q$: $∃x_{0}∈R$, such that $x_{0}^{2}+(a-1)x_{0}+1 < 0$. If $p$ or $q$ is true, and $p$ and $q$ are both false, find the range of values for the real number $a$.

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