
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 $$l: \begin{cases} x=2+ \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t \end{cases} (t \text{ is a parameter}),$$ and the curve $$C: \begin{cases} x=\cos\theta \\ y=\sin\theta \end{cases} (\theta \text{ is a parameter}).$$  
(1) Determine the positional relationship between $l$ and $C$;  
(2) If the x-coordinate of each point on curve $C_1$ is compressed to half of its original value, and the y-coordinate is compressed to $$\frac { \sqrt {3}}{2}$$ of its original value, resulting in curve $C_2$, let point $P$ be a moving point on curve $C_2$, find the minimum distance from it to the line $l$.

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