
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}_{0}\in\mathbb{R},x_{0}^{2}-ax_{0}+1=0 $", and $q$: "The range of the function $y={{x}^{2}}-2ax+{{a}^{2}}+1$ for $x\in[0,+\infty )$ is $[1,+\infty)$". If "$p\vee q$" is a false statement, find the range of values for the real number $a$.

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