
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases}x=-2+ \frac{1}{2}t \\ y= \frac{ \sqrt{3}}{2}t\end{cases}$ (with $t$ as the parameter). Taking the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_{1}$ is $r= \sqrt{6}$.

(Ⅰ) Write the standard equation of line $l$ and the parametric equation of curve $C_{1}$;

(Ⅱ) If the $x$-coordinates of the points on curve $C_{1}$ are shortened to $\frac{ \sqrt{6}}{6}$ times their original length, and the $y$-coordinates are shortened to $\frac{ \sqrt{2}}{2}$ times their original length, resulting in curve $C_{2}$, let point $P$ be any point on curve $C2$. Find the minimum distance from point $P$ to line $l$.

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