
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 equation of line $l$ is $x - y + 4 = 0$. The parametric equation of curve $C$ is $\begin{cases}x= \sqrt{3}\cos \alpha \\ y= \sqrt{2}\sin \alpha\end{cases}$ (where $\alpha$ is the parameter).

(Ⅰ) Given that in the polar coordinate system (with the same unit length as the Cartesian coordinate system $xOy$, and the origin $O$ as the pole, and the positive $x$-axis as the polar axis), the polar coordinates of point $P$ are $\left( \sqrt{2}, \frac{\pi}{4}\right)$. Determine the positional relationship between point $P$ and curve $C$.

(Ⅱ) Let point $Q$ be a moving point on curve $C$. Find the minimum distance from it to line $l$.

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