
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, 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 $a$.

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