
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 polar equation of curve $C$ is $2\rho\sin\theta+\rho\cos\rho=10$ and the curve $C_1$: 
$$
\begin{cases} 
x=3\cos\alpha \\ 
y=2\sin\alpha
\end{cases}
$$
(where $\alpha$ is a parameter).

(1) Find the general equation of curve $C_1$;  
(2) If point $M$ moves on curve $C_1$, find the minimum distance from $M$ to curve $C$.

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