
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 Cartesian plane $Oxy$, there is a line $l$ with the parametric equations $$\begin{cases} x=- \sqrt {5}+ \frac { \sqrt {2}}{2}t \\ y= \sqrt {5}+ \frac { \sqrt {2}}{2}t\end{cases}$$ (where $t$ is the parameter). Suppose we use point $O$ as the pole and the positive half of the x-axis as the polar axis to establish a polar coordinate system, the polar equation of curve $C$ is $\rho=4\cos \theta$.
(1) Find the rectangular coordinate equation of curve $C$ and the general equation of line $l$;
(2) If each point’s x-coordinate on curve $C$ is reduced to one half of its original value and then the resulting curve is translated 1 unit to the left, we get a new curve $C_1$. Find the minimum distance from the points on curve $C_1$ to line $l$.

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