
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
The polar equation of curve C is given by $\rho=4\sin \theta$. Let the parametric equation of line l be $\begin{cases} x=t-1 \\ y=2t+1\end{cases}$ (where t is the parameter).  
(i) Convert the polar equation of curve C to a Cartesian coordinate equation;  
(ii) Let M and N be the intersection points of line l and curve C, with O being the origin. Compute the area of triangle $\triangle OMN$.

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