
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 $$\begin{cases} x= \sqrt {3}\cos\theta \\ y=\sin\theta \end{cases}$$, and in the polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve $C_2$ is $\rho\sin\left(\theta+ \frac {\pi}{4}\right)=2 \sqrt {2}$.  
(1) Write the general equation of $C_1$ and the Cartesian coordinate equation of $C_2$;  
(2) Suppose point $P$ is on $C_1$, and point $Q$ is on $C_2$, find the minimum value of $|PQ|$.

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