
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
Given the curve $C$ with the polar coordinate equation $2\rho\sin \theta+\rho\cos \theta=10$, curve $C_{1}$ is defined by the parametric equations $\begin{cases} x=\cos \alpha \\ y=\sin \alpha \end{cases}$ where $\alpha$ is a parameter. Curve $C_{1}$ undergoes a scaling transformation $\begin{cases} x'=3x \\ y'=2y \end{cases}$ to obtain curve $C_{2}$.

1. Find the parametric equations of curve $C_{2}$.
2. If point $M$ moves along curve $C_{2}$, find the minimum distance from point $M$ to curve $C$.

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