
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
The minimum distance from a point on the graph of the function $y=f(x)$ to the origin is called the "central distance" of the function $y=f(x)$. It is known that the "central distance" of the function $g(x)=x+\frac{a}{x}$ (where $a>0$) is not less than $\sqrt{2}$. The range of the real number $a$ is _______.

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