
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 circle $C_1$ is given by $\begin{cases} x=2\cos\alpha \\ y=2+2\sin\alpha \end{cases}$ ($\alpha$ is the parameter), and the polar coordinate equation of circle $C_2$ with the origin $O$ as the pole and the positive $x$-axis as the polar axis is given by $\rho = 2\sqrt{2}\cos(\theta + \frac{\pi}{4})$.

(I) Find the standard form equation of circle $C_1$ and the rectangular coordinate equation of circle $C_2$.
(II) Determine the positional relationship between circles $C_1$ and $C_2$.

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