
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 $l$: $\begin{cases} x=1+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}(t$ is a parameter$)$, and the curve $C_{1}$: $\begin{cases}x=\cos \theta \\ y=\sin \theta\end{cases} (\theta$ is a parameter$)$.
- (I) Suppose $l$ intersects $C_{1}$ at points $A$ and $B$, find $|AB|$;
- (II) If the x-coordinates of the points on curve $C_{1}$ are compressed to half of their original values, and the y-coordinates are compressed to $\frac {\sqrt {3}}{2}$ of their original values, resulting in curve $C_{2}$, suppose point $P$ is 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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