
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
The minimum distance from a point P on the circle $C: \begin{cases} x=\cos\theta, \\ y=1+\sin\theta \end{cases}$ (where $\theta$ is a parameter) to the line $l: \begin{cases} x=1+2t, \\ y=-1+t \end{cases}$ (where $t$ is a parameter) is $\_\_\_\_\_\_$.

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