
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 Cartesian coordinate system $xOy$, point $P(2,0)$ is given, and the curve $C$ has the parametric equations $\begin{cases} x=4t^{2} \\ y=4t \end{cases}$ (where $t$ is the parameter). A polar coordinate system is established with the origin as the pole and the positive $x$-axis as the polar axis.  
(Ⅰ) Find the general equation and the polar equation of curve $C$;  
(Ⅱ) A line $l$ passing through point $P$ with an inclination angle of $\dfrac{\pi}{4}$ intersects curve $C$ at points $A$ and $B$. Find $|AB|$.

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