
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 $\rho-4\sin \theta=0$. With the pole as the origin and the positive half-axis of the $x$-axis as the polar axis, a Cartesian coordinate system is established. Line $l$ passes through point $M(1,0)$ with an inclination angle of $\dfrac{3\pi}{4}$.
$(1)$ Find the Cartesian equation of curve $C$ and the parametric equation of line $l$;
$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, calculate $|MA|+|MB|$.

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