
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 Cartesian coordinate plane $(xOy)$, the equation of line $l$ is $x+y-6=0$. The parametric equation of circle $C$ is $ \begin{cases} x=2\cos \theta \\ y=2\sin \theta +2 \end{cases}(\theta \in[0,2\pi))$. Determine the distance between the center of circle $C$ and line $l$.

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