
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 system $xOy$, the parametric equation of line $l$ is $\begin{cases} x= \frac {1}{2}t \\ y=m+ \frac { \sqrt {3}}{2}t\end{cases}$ (where $t$ is the parameter), and in the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $\rho^{2}-2\rho\cos \theta-4=0$  
$(1)$ If line $l$ and curve $C$ have no common points, find the range of $m$;  
$(2)$ If $m=0$, find the length of the chord cut by curve $C$ on line $l$.

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