
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]


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In the Cartesian coordinate system $xoy$, the parametric equation of curve $C_1$ is $$\begin{cases} x= \sqrt {3}\cos\alpha \\ y=\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter). Taking the origin $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_2$ is $$\rho\sin(\theta- \frac {\pi}{4})=2 \sqrt {2}$$.
(1) Find the general equation of curve $C_1$ and the Cartesian equation of curve $C_2$;
(2) Let $P$ be a moving point on curve $C_1$. Find the minimum distance from point $P$ to points on curve $C_2$.

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