
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
Selective 4-4: Coordinate Systems and Parametric Equations

In the rectangular coordinate system, the parametric equations of the curve $C$ are given by $\begin{cases} x = 1 + 2 \cos \phi \\ y = 1 + 2 \sin \phi \end{cases}$ (where $\phi$ is a parameter). Establish a polar coordinate system with the origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of line $l$ is given by $\rho = \dfrac{4}{\cos \theta - \sin \theta}$.

(1) Find the Cartesian equation of curve $C$ and the rectangular coordinate equation of line $l$.

(2) Determine if there is a point $P$ on curve $C$ such that the distance from point $P$ to line $l$ is minimal. If such a point exists, find the minimum distance and the rectangular coordinates of point $P$. If not, explain why.

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