
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 parametric equation of curve $C$ is 
$$
\begin{cases} 
x=4\cos \theta \\ 
y=3\sin \theta
\end{cases}
(\theta \text{ is the parameter}).
$$

(1) Find the Cartesian equation of curve $C$;  
(2) Draw line $l$ through point $M(0,1)$ intersecting curve $C$ at points $A$ and $B$ (with $A$ above $B$), and satisfying $BM=2AM$. Find the equation of line $l$.

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