
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 plane, with the origin O as the pole and the non-negative half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that the polar coordinates of point M are $(4\sqrt{2}, \frac{\pi}{4})$. The parametric equation of curve C is
$$
\begin{cases} 
x=1+ \sqrt{2}\cos\alpha \\
y= \sqrt{2}\sin\alpha 
\end{cases} \quad (\alpha \text{ is the parameter}).
$$
(I) Find the rectangular (Cartesian) coordinate equation of line OM;  
(II) Find the minimum distance from point M to the points on curve C.

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