
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
(Optional Course 4-4: Coordinate Systems and Parametric Equations)

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

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