
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 line $l$ as $\rho \cos (\theta + \frac{\pi }{4})=4\sqrt{2}$, and the parametric equations of circle $M$ as $\begin{cases} x=1+\sqrt{2}\cos \theta \\ y=-1+\sqrt{2}\sin \theta \end{cases}$ (where $\theta$ is the parameter), find the minimum distance from points on circle $M$ to line $l$.

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