
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) Using the same unit length as the Cartesian coordinate system $xoy$ and the origin $O$ as the pole, with the positive semiaxis of the $x$-axis as the polar axis, find the polar coordinate equation of line $l$.

(2) Let $Q$ be a moving point on curve $C$, find the minimum distance between point $Q$ and line $l$.

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