
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 equation of line $l$ is $\begin{cases} x=t+1 \\ y=t+4 \end{cases} (t \text{ is the parameter})$, and 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 $\rho= \frac{\sqrt{3}}{\sqrt{1+2\cos^2 \theta}}$.
(1) Write the general equation of line $l$ and the standard equation of curve $C$ in rectangular coordinates;
(2) Let $d$ be the distance from a point on curve $C$ to line $l$, find the range of $d$.

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