
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 that in the rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is: $\begin{cases} & x=1-\frac{\sqrt{2}}{2}t, \ & y=2+\frac{\sqrt{2}}{2}t, \ \end{cases}$ ($t$ is the parameter). Establish a polar coordinate system with $Ox$ as the polar axis. The polar coordinate equation of circle $C$ is: $ρ=2\cos θ$. The minimum distance from the points on circle $C$ to line $l$ is _______.

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