
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
The parametric equation of the ellipse $C$ is $\begin{cases} x=2\cos \phi \\ y=\sin \phi \end{cases}$ ($\phi$ is the parameter), with the origin of the Cartesian coordinate system as the pole and the positive half-axis of $x$ as the polar axis. In polar coordinates, the equation of line $l$ is $\rho= \frac {10}{2\cos \theta +\sin \theta }$.  
$(1)$ Find the equation of $l$ in the Cartesian coordinate system and the standard equation of the ellipse $C$;  
$(2)$ There is a moving point $M$ on the ellipse $C$, find the minimum distance from $M$ to $l$ and the coordinates of $M$ at this time.

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