
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 $\begin{cases} & x=m+2t \\ & y=4t \end{cases}$ ($m$ is a constant, $t$ is the parameter), and the parametric equation of curve $C$ as $\begin{cases} & x=\sqrt{5}\cos \theta \\ & y=\sqrt{5}\sin \theta \end{cases}$ ($\theta$ is the parameter).

$(1)$ Find the general equation of line $l$ and curve $C$;

$(2)$ If line $l$ and curve $C$ have common points, find the range of the real number $m$.

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