
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 system $xOy$, the equation of line $l$ is $x + y - 6 = 0$. The parametric equation of circle $C$ is
$$
\begin{cases} 
x = 2\cos\theta \\
y = 2\sin\theta + 2
\end{cases}
\quad (\theta \in [0, 2\pi)).
$$
Find the distance from the center of circle $C$ to the line $l$.

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