
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 functions $f(x)=\frac{8x}{1+{x}^{2}}$ and $g\left(x\right)=x^{2}-ax+1$, if there exists $a\in R$ such that for any $x_{1}\in \left[0,+\infty \right)$, there exists a unique $x_{0}\in \left[-1,2\right]$ satisfying $f(x_{1})=g(x_{0})$, then the range of $a$ is ______.

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