
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
(Elective 4-4: Coordinate Systems and Parametric Equations)
In the rectangular coordinate system $xOy$, establish a polar coordinate system with coordinate origin $O$ as the pole and the positive semi-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 $\begin{cases} x = 3\cos\theta \\ y = 2\sin\theta \end{cases}$ ($\theta$ is the parameter, $\theta \in \mathbb{R}$).

1. Write the Cartesian equations for $l$ and $C$.
2. Find the point $M$ on $C$ such that the distance from $M$ to $l$ is a minimum, and find the minimum value.

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