
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 a function $f(x)=\left\{\begin{array}{l}{\frac{x}{2{x}^{2}+8}, x≥2}\\{(\frac{1}{2})^{|x-a|}, x＜2}\end{array}\right.$, if for any $x_{1}\in [2,+\infty)$, there exists a unique $x_{2}\in (-\infty, 2)$ such that $f(x_{1})=f(x_{2})$, then the range of real number $a$ is ____.

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