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

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