
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 $(xOy)$, taking $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system with the same unit length. Given that the parametric equation of curve $(C_{1})$ is $\begin{cases}x= \sqrt{3}+2\cos α \\ y=3+2\sin α\end{cases}(α∈[0,2π],α)$ and the polar coordinate equation of curve $(C_{2})$ is $ρ\sin \left(θ+ \dfrac{π}{3}\right)=α (α∈R)$. If curves $(C_{1})$ and $(C_{2})$ have exactly one common point, find the value of real number $α$.

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