
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 Cartesian coordinate system $xoy$, there is a line $l$: $y=2x-4$, and a circle $C$ with a radius of $1$. The center of circle $C$ is located on line $l$. If there exists a point $M$ on circle $C$ that is also on circle $D$: $x^{2}+(y+1)^{2}=4$, determine the range of the possible values for the x-coordinate $a$ of the center of circle $C$.

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