
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 $l$: $\begin{cases}x=1+t \\ y=\sqrt {3}t\end{cases}(t\text{ is a parameter})$, and the curve $C_{1}$: $\begin{cases}x=2\cos \theta \\ y=2\sin \theta\end{cases}(\theta\text{ is a parameter})$,
(1) Find the value of $|AB|$, where $A$ and $B$ are the intersection points of line $l$ and curve $C_{1}$;
(2) If the horizontal coordinates of each point on curve $C_{1}$ are compressed to $\frac {1}{4}$ of their original values, and the vertical coordinates are compressed to $\frac {\sqrt {3}}{4}$ of their original values, forming a new curve $C_{2}$, find the minimum distance from a moving point $P$ on curve $C_{2}$ to line $l$.

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