
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 rectangular coordinate system xOy, the parametric equations of curve C1 are given by $$\begin{cases} x=\cos\alpha, \\ y=\sqrt{3}\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of curve C2 is given by $$\rho \sin \left( \theta - \frac{\pi }{4} \right) = 2\sqrt{2}$$.

1. Write the Cartesian equation of C1 and the rectangular coordinate equation of C2.
2. Let point P be on C1 and point Q be on C2. Find the minimum value of |PQ| and the rectangular coordinates of P in this case.

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