
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 the pole of the polar coordinate system is at the origin of the Cartesian coordinate system, and the polar axis coincides with the non-negative half-axis of the $x$-axis, the parametric equation of line $l$ is:

\[
\begin{cases} 
& x=-1+\dfrac{\sqrt{3}}{2}t \\
& y=\dfrac{1}{2}t \\
\end{cases} \quad (t \text{ is the parameter})
\]

The polar equation of curve $C$ is: $\rho =4\cos \theta$.

(Ⅰ) Write the Cartesian coordinate equation of curve $C$ and the general equation of line $l$;

(Ⅱ) Suppose line $l$ intersects curve $C$ at points $P$ and $Q$, find the value of $|PQ|$.

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