
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 curve $C_1$ is 
$$
\begin{cases} 
x= \sqrt {2}\cos\alpha \\ 
y=\sin\alpha
\end{cases}
$$
($\alpha$ is the parameter). Taking the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of curve $C_2$ is $\rho\sin\left(\pi+ \frac {\pi}{4}\right)=4 \sqrt {2}$.

(I) Find the general equation of curve $C_1$ and the Cartesian equation of curve $C_2$;  
(II) Let $P$ be a moving point on curve $C_1$, find the minimum value of the distance from point $P$ to curve $C_2$.

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