
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 $x - y + 4 = 0$, and the parametric equations of curve $C$ are given by $\begin{cases} x = \sqrt{3} \cos \alpha \\ y = \sin \alpha \end{cases}$ where $\alpha$ is the parameter.

1. Given that the polar coordinate system has the same length unit as the Cartesian coordinate system $(xOy)$, with the origin $O$ as the pole and the nonnegative $x$-axis as the polar axis, the polar coordinates of point $P$ are $\left(4, \frac{\pi}{2}\right)$. Determine the relationship between point $P$ and line $l$.
2. Let point $Q$ be a moving point on curve $C$. Find the minimum distance from point $Q$ to line $l$.

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