
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, the line $l$: $\begin{cases} x=2+t\cos α \\ y=1+t\sin α \end{cases} (t$ is a parameter, $0\leqslant α < π)$, intersects the curve $C$: $ρ=4\cos θ$ in the polar coordinate system with the pole at $O$ and the positive half of the $x$-axis as the polar axis.
(I) Find the Cartesian equation of the curve $C$;
(II) Given the point $P(2,1)$, if the line $l$ intersects the curve $C$ at points $A$ and $B$, and $\overrightarrow{AP}=2 \overrightarrow{PB}$, find $\tan α$.

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