
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 rectangular coordinate system xoy, the parametric equation of the line $l$ is:
$$
\begin{cases}
x = t - 3 \\
y = \sqrt{3}t
\end{cases}
\quad (t \text{ is the parameter})
$$
Taking the origin $O$ of the rectangular coordinate system xOy as the pole and the non-negative half-axis of x as the polar axis, the polar equation of circle C is $\rho^2 - 4\rho\cos\theta + 3 = 0$. The distance from the center $C$ of the circle to the line $l$ is __________.

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