
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 plane rectangular coordinate system, establish a polar coordinate system with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C$ is $2ρ\sin θ+ρ\cos θ=10$. The parametric equation of the curve $C\_1$ is $\begin{cases} x=3\cos α \ y=2\sin α \end{cases}$ ($α$ is the parameter).

1. Find the Cartesian equation of the curve $C\_1$.
2. If point $M$ moves on the curve $C\_1$, find the minimum distance from $M$ to the curve $C$.

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