
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 that in the rectangular coordinate system $(xOy)$, the parametric equations of circle $C$ are $\begin{cases}x=1+2\cos θ \\\\ y=2\sin θ\end{cases}(θ \text{ is the parameter})$,

(1) Establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis, and derive the polar equation of circle $C$;

(2) The polar equation of line $l$ is $θ= \dfrac{π}{3}$, and line $l$ intersects with circle $C$ at points $A$ and $B$. Calculate the length of chord $AB$.

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