
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 polar coordinate system, the polar equations of line $l$ and circle $C$ are $\rho\cos (\theta+ \frac {\pi}{6})=a(a\in\mathbb{R})$ and $\rho=4\sin \theta$, respectively. If line $l$ and circle $C$ have exactly one common point, find the value of $a$.

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