
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, with the origin as the pole and the non-negative half-axis of the $x$-axis as the polar axis, and taking the same unit length, a polar coordinate system is established. The polar equation of curve $C$ is: $\rho=2\cos \theta$.

$(I)$ If the curve $C_{2}$ has the parametric equation: $\begin{cases} x=t\cos \alpha \\ y=1+t\sin \alpha \end{cases}$ ($\alpha$ is a parameter), find the Cartesian equation of curve $C_{1}$ and the general equation of curve $C_{2}$.

$(II)$ If the curve $C_{2}$ has the parametric equation: $\begin{cases} x=t\cos \alpha \\ y=1+t\sin \alpha \end{cases}$ ($t$ is a parameter), $A(0,1)$, and the intersection points of curve $C_{1}$ and curve $C_{2}$ are $P$ and $Q$, find the range of values for $\dfrac {1}{|AP|}+ \dfrac {1}{|AQ|}$.

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