
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 $xOy$, with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. The parametric equation of curve $C_1$ is $$\begin{cases} x=2 \sqrt {2}\cos\alpha \\ y=2\sin\alpha \end{cases}(\alpha\in\mathbb{R}, \alpha \text{ as the parameter}),$$ and the polar equation of curve $C_2$ is $$\rho\cos\theta- \sqrt {2}\rho\sin\theta-5=0.$$  
(1) Find the standard equation of curve $C_1$ and the Cartesian coordinate equation of curve $C_2$;  
(2) Let $P$ be a point on curve $C_1$ and $Q$ a point on curve $C_2$, find the minimum value of $|PQ|$.

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