
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
In the Cartesian coordinate plane $xoy$, let circle $M$ have a radius of $1$, and its center lies on the line $2x-y-4=0$. If there does not exist a point $N$ on circle $M$ such that $NO=\frac{1}{2}NA$, where $A(0,3)$, then the range of the abscissa of the center $M$ is _____.

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