<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 In the polar coordinate system, let line $l$ pass through points $A\left( \sqrt {3}, \dfrac {\pi}{6}\right)$ and $B(3,0)$, and suppose that line $l$ and curve $C$: $\rho=a\cos \theta$ ($a > 0$) have exactly one point in common. Find the value of the real number $a$. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
6
In the polar coordinate system, let line $l$ pass through points $A\left( \sqrt {3}, \dfrac {\pi}{6}\right)$ and $B(3,0)$, and suppose that line $l$ and curve $C$: $\rho=a\cos \theta$ ($a > 0$) have exactly one point in common. Find the value of the real number $a$.
test