
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
Elective 4-4: Coordinate System and Parametric Equations

In the polar coordinate system, the polar equation of curve $C$ is $\rho^{2}(1+2\sin^{2}\theta)=3$. A Cartesian coordinate system is established with the pole as the origin and the positive half-axis of the polar axis as the $x$-axis. The parametric equation of line $l$ is $\begin{cases} & x=t \\ & y=6+t \end{cases}$ (where $t$ is the parameter).

(Ⅰ) Write the parametric equation of curve $C$ and the general equation of line $l$;

(Ⅱ) Given that point $P$ is a point on curve $C$, find the minimum distance from point $P$ to line $l$.

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