
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 the line $l_{1}$ is $\begin{cases}x=t- \sqrt{3} \\ y=kt\end{cases}$ (where $t$ is the parameter), and the parametric equation of line $l_{2}$ is $\begin{cases}x= \sqrt{3}-m \\ y= \frac{m}{3k}\end{cases}$ (where $m$ is the parameter). Let $P$ be the intersection point of $l_{1}$ and $l_{2}$. As $k$ varies, the trajectory of $P$ is the curve $C_{1}$.

(Ⅰ) Write the general equation and the parametric equation of $C_{1}$;

(Ⅱ) Establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, and let the polar equation of curve $C_{2}$ be $\rho \sin \left( \theta +\frac{\pi}{4} \right)=4\sqrt{2}$. If $Q$ is a moving point on curve $C_{1}$, find the minimum distance from point $Q$ to $C_{2}$.

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