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

(1) Find the rectangular coordinate equation of circle $C$.
(2) Suppose 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}
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