
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, the circle $C_1$ with equation $x^2+y^2=1$ undergoes a scaling transformation $$\begin{cases} x'=3x \\ y'=2y \end{cases}$$ to obtain the curve $C_2$. With the origin as the pole and the positive half-axis of the x-axis as the polar axis, and by choosing the same unit length in both coordinate systems, a polar coordinate system is established, where the polar equation of the line $l$ is $\cos\theta+2\sin\theta=\frac{10}{\rho}$.  
(1) Find the Cartesian equation of curve $C_2$ and the Cartesian equation of line $l$;  
(2) Find a point $M$ on curve $C_2$ such that the distance from point $M$ to line $l$ is minimized, and calculate the minimum distance.

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