
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]


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In the Cartesian coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=1-\frac{\sqrt{2}}{2}t \\ y=4-\frac{\sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter). In the polar coordinate system established on the origin as the pole, the positive $x$-axis as the polar axis, and having the same unit length as the Cartesian coordinate system, the equation of circle $C$ is $\rho=4\sin\theta$.

1. Find the Cartesian equation of circle $C$.
2. If circle $C$ intersects line $l$ at points $A$ and $B$, and the coordinates of point $M$ are $(1,4)$, find the value of $|MA|+|MB|$.

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