
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 $\begin{cases} & x=t-1 \\ & y=t+2 \\ \end{cases} (t \text{ is a parameter})$. In the polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of curve $C$ is given by $\rho = \frac{\sqrt{3}}{\sqrt{1+2\cos^2 \theta}}$.
(1) Directly write out the general equation of line $l$ and the rectangular coordinate equation of curve $C$;
(2) If the distance between a point on curve $C$ and line $l$ is denoted as $d$, find the range of $d$.

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