
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 $x O y$, point $A(0,3)$ and line $l: y = 2x - 4$ are given. Let $\odot C$ be a circle with radius 1 and center located on line $l$. If there exists a point $M$ on $\odot C$ such that $|MA| = 2|MO|$, then the range of values for the x-coordinate $a$ of the center $C$ is $\qquad$.

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