
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 curve $C$ with the polar coordinate equation $\rho= \frac{4\cos \theta}{\sin^{2}\theta}$, and the line $l$ with the parametric equations $x=t\cos \alpha, y=1+t\sin \alpha$ ($t$ is the parameter, $0\leqslant \alpha < \pi$).
(I) Convert the polar coordinate equation of the curve $C$ to a rectangular coordinate equation and describe the shape of the curve $C$.
(II) If the line $l$ passes through the point $(1,0)$, find the length of the line segment $AB$ intercepted by the curve $C$.

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