
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 $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of line $l$ is $\rho(\cos \theta + 2\sin \theta) = 10$, and the parametric equation of curve $C$ is $\begin{cases} x=3\cos \theta \\ y=2\sin \theta \end{cases}$ (with $\theta$ as the parameter, $\theta \in \mathbb{R}$).  
$(1)$ Write the standard equations of $l$ and $C$;  
$(2)$ Find the point $M$ on $C$ such that the distance from $M$ to $l$ is minimized, and find the minimum value.

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