
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 $xOy$, with $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. For curve $C$: $\rho^2 - 4\rho\cos\theta + 1 = 0$, and line $l$: 
$$
\begin{cases} 
x=4+t\sin\alpha \\
y=t\cos\alpha 
\end{cases}
$$
(where $t$ is a parameter, $0 \leq \alpha < \pi$).

(1) Find the parametric equation of curve $C$;  
(2) If line $l$ is tangent to curve $C$, find the slope angle of line $l$ and the coordinates of the tangent point.

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