
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 
$$
\begin{cases}
x = \sqrt {2} \sin(\alpha + \frac {\pi}{4}) \\
y = \sin{2\alpha} + 1
\end{cases}
$$
(where $\alpha$ is the parameter). Using O as the pole and the positive x-axis as the polar axis, we establish the polar coordinate system for curve $C_2$ with the polar equation $\rho^2 = 4\rho \sin{\theta} - 3$.

(Ⅰ) Find the Cartesian equations for curves $C_1$ and $C_2$.
(Ⅱ) Find the minimum distance between any point on curve $C_1$ and any point on curve $C_2$.

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