
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 line $l:\begin{cases} & x=t \\\\ & y=1+t \\\\ \\end{cases}$ and the circle $C$: $\rho =2\cos \theta$, find the distance between the center of the circle $C$ and the line $l$.

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