
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 rectangular coordinate system $(xOy)$, a pole coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The curve $C$: $ρ^{2}-4ρ\cos θ+1=0$, and the line $l$: $ \begin{cases} x=4+t\sin α \\ y=t\cos α \end{cases} (t$ is a parameter, $0≤α < π)$.
(1) Find the parametric equation of the curve $C$;
(2) If the line $l$ is tangent to the curve $C$, find the slope angle and the coordinates of the tangent point.

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