
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]


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Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} & x=t-1, \\ & y=t+2, \\ \end{cases}(t$ is the parameter$).$ In the polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C$ is $\rho =\dfrac{\sqrt{3}}{\sqrt{1+2\cos^2\theta }}.$

(Ⅰ) Directly write out the Cartesian equations of line $l$ and curve $C$;

(Ⅱ) Let the distance from a point on curve $C$ to line $l$ be $d$, find the range of $d$.

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