
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 that in the rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are $\begin{cases} x=t-3 \ y=\sqrt{3}t \end{cases}(t\text{ is a parameter})$ and in the polar coordinate system $((\text{ with the same unit length as the rectangular coordinate system }xOy\text{, and with the origin }O\text{ as the pole, and the positive half of the }x\text{-axis as the polar axis})$, the polar equation of curve $C$ is $ρ^{2}=4ρ\cos θ-3$.

(1) Find the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C$.
(2) Let point $P$ be a moving point on curve $C$, find the range of its distance to line $l$.

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