
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
Suppose $4-4$: Coordinate System and Parametric Equations

In the rectangular coordinate system $xOy$, a polar coordinate system is established with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of line $l$ is $\rho (\cos \theta + 2\sin \theta) = 10$, and the parametric equation of curve $C$ is $\begin{cases} & x=3\cos \varphi \\\ & y=2\sin \varphi \end{cases} (\varphi \text{ is the parameter, } \varphi \in \mathbb{R}).$

(I) Write the rectangular coordinate equation of line $l$ and the ordinary equation of curve $C$;

(II) Find the point $M$ on $C$ such that the distance from point $M$ to $l$ is the smallest, and find the smallest value.

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