
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 a circle $C$: $(x-2)^{2}+y^{2}=4$, and a line $l$ passing through $M(1,0)$ with an inclination angle of $\dfrac {5\pi}{6}$. The line $l$ intersects the circle $C$ at points $A$ and $B$.
$(1)$ If the origin of the Cartesian coordinate system is taken as the pole and the positive half-axis of $x$ as the polar axis, without changing the unit of length, establish a polar coordinate system and write the polar equation of circle $C$;
$(2)$ Choose an appropriate parameter, write a parametric equation for line $l$, and calculate the value of $|MA|+|MB|$.

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