
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
In the rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=-\sqrt{5}+\frac{\sqrt{2}}{2}t \\ y=\sqrt{5}+\frac{\sqrt{2}}{2}t \end{cases} \; (t \text{ is the parameter})$. If the origin $O$ is taken as the pole and the positive half of the $x$-axis as the polar axis to establish a polar coordinate system, then the polar equation of curve $C$ is $\rho=4\cos\theta$.
(1) Find the rectangular coordinate equation of curve $C$ and the general form equation of line $l$;
(2) By shrinking the abscissa of each point on curve $C$ to half of the original length and then translating the resulting curve 1 unit to the left, we obtain curve $C_{1}$. Find the minimum distance between points on curve $C_{1}$ and line $l$.

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