
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 equation of line $l$ as $\begin{cases} & x=-1+t\cos \alpha, \\ & y=1+t\sin \alpha \end{cases} (t \text{ is the parameter})$, the parametric equation of curve $C_{1}$ as $\begin{cases} & x=2+2\cos t, \\ & y=4+2\sin t \end{cases} (t \text{ is the parameter})$, and the polar equation of curve $C_{2}$ as $\rho=4\cos \theta$ with the origin as the pole and the positive semi-axis of $x$ as the polar axis.

(1) If the slope of line $l$ is $2$, determine the positional relationship between line $l$ and curve $C_{1}$;

(2) Find the polar coordinates $(\rho\geqslant 0,0\leqslant \theta < 2\pi)$ of the intersection point(s) of $C_{1}$ and $C_{2}$.

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