
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 $l: \begin{cases} x=2+ \frac{ \sqrt {2}}{2}t\\y= \frac{ \sqrt {2}}{2}t\end{cases} (t$ is a parameter$)$ and the curve $C: \begin{cases} x=\cos \theta \\y=\sin \theta \end{cases} (\theta$ is a parameter$)$,

(1) Determine the relationship between $l$ and $C$;

(2) If the horizontal coordinates of a point on the curve $C_{1}$ are compressed to $\frac {1}{2}$ of the original, and the vertical coordinates are compressed to $\frac { \sqrt {3}}{2}$ of the original, a new curve $C_{2}$ is obtained. Let $P$ be a moving point on the curve $C_{2}$, find the minimum distance from $P$ to the line $l$.

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