
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 equation of line $l$ as $\begin{cases}x=-1-\frac{\sqrt{2}}{2}t, \\ y=\frac{\sqrt{2}}{2}t\end{cases}$ ($t$ is the parameter), and point $P$ is any point on the curve $\begin{cases}x=1+2\cos\alpha, \\ y=2+2\sin\alpha\end{cases}$ ($\alpha$ is the parameter), find the minimum distance from point $P$ to line $l$.

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