
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
Given the parametric equations of line $l$ as $\begin{cases} x = t \\ y = t + 1 \end{cases}$ (where $t$ is the parameter), with the origin as the pole and the positive x-axis as the polar axis, the polar equation of circle $C$ is $\rho = -6\cos\theta$. Determine the distance from the center of circle $C$ to line $l$.

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