
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 $l: x-y+4=0$ and the circle $C: \left\{\begin{array}{l}{x=1+2\cos\theta}\\{y=1+2\sin\theta}\end{array}\right.$, calculate the minimum distance from any point on circle $C$ to line $l$.

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