
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 coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases}x=t+1 \\ y=t+4\end{cases} (t$ 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 $\rho= \dfrac{ \sqrt{3}}{ \sqrt{1+2{\cos }^{2}\theta}}$．  
$(1)$ Write the general equation of line $l$ and the standard equation of curve $C$ in Cartesian coordinates;  
$(2)$ 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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