
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 equations of line $l$ are $$\begin{cases} x=m+2t, \\ y= \sqrt {2}t\end{cases}$$ ($t$ is the parameter), and the polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C$ is $\rho^2 = \frac {4}{1+\sin^{2}\theta }$.
   (I) Find the Cartesian equation of line $l$ and curve $C$;
   (II) Let $P$ be a point on curve $C$, $PQ \perp l$, with $Q$ being the foot of the perpendicular. If the minimum value of $|PQ|$ is $2$, find the value of $m$.

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