
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
Taking the origin of the Cartesian coordinate system $xOy$ as the pole and the non-negative half-axis of the $x$ axis as the polar axis, with the same unit of length for both coordinate systems. The parametric equation of curve $C_1$ is: 
$$
\begin{cases} 
x=2\cos \theta \\
y=2\sin \theta 
\end{cases} (\theta \text{ as the parameter})
$$
By changing the ordinate of each point on curve $C_1$ to half of its original value (the abscissa remains unchanged), curve $C_2$ is obtained. The polar equation of line $l$ is: 
$$
\sqrt {3}\rho\cos \theta+2\rho\sin \theta+m=0.
$$
(Ⅰ) Find the parametric equation of curve $C_2$;  
(Ⅱ) If the maximum distance from a point on curve $C_2$ to line $l$ is $2 \sqrt {7}$, find the value of $m$.

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