
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
Given the polar coordinate equation of a line as $\rho \sin (\theta + \frac{\pi }{4})=\frac{\sqrt{2}}{2}$, and the parametric equation of circle $M$ as $\begin{cases} & x=2\cos \theta \\ & y=-2+2\sin \theta \\ \end{cases}$ (where $\theta$ is the parameter). Establish a rectangular coordinate system with the pole $O$ as the coordinate origin and the positive half of the $x$-axis as the polar axis.

(I) Convert the polar coordinate equation of the line to a rectangular coordinate equation.
(II) Find the minimum distance from a point on circle $M$ to the line.

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