
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 parametric equation of line $l$ as $\begin{cases} x=a-2t \\ y=-4t \end{cases}$, ($t$ is the parameter), and the parametric equation of circle $C$ as $\begin{cases} x=4\cos \theta \\ y=4\sin \theta \end{cases}$, ($\theta$ is a constant).

 $(I)$ Find the general equation of line $l$ and circle $C$;

 $(II)$ If line $l$ and circle $C$ have common points, find the range of the real number $a$.

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