
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 parametric equations of line $l$ as $\begin{cases} x=t\cos α \\ y=1+t\sin α \end{cases}\left(t \text{ is a parameter, } \frac{π}{2}\leqslant α < π\right)$, a polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of circle $C$ is $ρ =2\cos θ$.
(I) Discuss the number of common points between line $l$ and circle $C$;
(II) Draw a perpendicular line to line $l$ passing through the pole, with the foot of the perpendicular denoted as $P$, find the length of the chord formed by the intersection of the trajectory of point $P$ and circle $C$.

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